Updated on 2024/02/28

写真a

 
TANIGUCHI, Masanobu
 
Affiliation
Faculty of Science and Engineering
Job title
Professor Emeritus
Degree
Doctor of Engineering ( Osaka University )

Education Background

  •  
    -
    1974

    Osaka University   Faculty of Science   Mathematics  

Professional Memberships

  •  
     
     

    日本統計学会

  •  
     
     

    日本数学会

  •  
     
     

    International Statistical Institute

  •  
     
     

    Institute of Mathematical Statistics

Research Areas

  • Applied mathematics and statistics

Research Interests

  • Time series analysis, Mathematical Statistics, Econometrics, Financial Engineering, Information geometry

Awards

  • Analysis Award

    2012.09  

  • Japan Statistical Society Prize

    2004.09  

  • Econometric Theory Award

    2000  

  • Ogawa Prize

    1989  

 

Papers

  • Testing for Granger causality by use of Box-Cox transformations

    小池隆之介, Dou Xiaoling, 谷口正信, Xue Yujie

    ASTE Special Issue on the “Financial & Pension Mathematical Science”   13   17 - 23  2016.03  [Refereed]

  • Asymptotics of realized volatility with non-Gaussian ARCH(∞) microstructure noise

    Hiroyuki Taniai, Takashi Usami, Nobuyuki Suto, Masanobu Taniguchi

    Journal of Financial Econometrics   10 ( 4 ) 617 - 636  2012.09

     View Summary

    In order to estimate the conditional variance of some specific day, the sum of squared intraday returns, as known as "realized volatility" (RV) or "realized variance," is often used. Although this estimator does not converge to the true volatility when the observed price involves market microstructure noise, some subsample-based estimator is known to resolve this problem. In this paper, we will study the asymptotics of this estimator, assuming that market microstructure noise follows a non-Gaussian autoregressive conditional heteroskedastic model of order ∞ (ARCH(∞)). There we elucidate the asymptotics of RV and subsample estimator, which are influenced by the non-Gaussianity and dependent structure of the noise. Some numerical studies are given, and they illuminate interesting features of the asymptotics. © The Author, 2012. Published by Oxford University Press. All rights reserved.

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    Scopus

    2
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  • JACKKNIFED WHITTLE ESTIMATORS

    Masanobu Taniguchi, Kenichiro Tamaki, Thomas J. DiCiccio, Anna Clara Monti

    STATISTICA SINICA   22 ( 3 ) 1287 - 1304  2012.07  [Refereed]

     View Summary

    The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

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  • Generalized information criterion

    Masanobu Taniguchi, Junichi Hirukawa

    JOURNAL OF TIME SERIES ANALYSIS   33 ( 2 ) 287 - 297  2012.03  [Refereed]

     View Summary

    In this article, we propose a generalized Akaike's information criterion (AIC) (GAIC), which includes the usual AIC as a special case, for general class of stochastic models (i.e. i.i.d., non-i.i.d., time series models etc.). Then we derive the asymptotic distribution of selected order by GAIC, and show that is inconsistent, i.e. (true order). This is the problem of selection by completely specified models. In practice, it is natural to suppose that the true model g would be incompletely specified by uncertain prior information, and be contiguous to a fundamental parametric model with dim 0 = p0. One plausible parametric description for g is , h = (h1, ... ,hK - p0) where n is the sample size, and the true order is K. Under this setting, we derive the asymptotic distribution of . Then it is shown that GAIC has admissible properties for perturbation of models with order of , where the length h is large. This observation seems important. Also numerical studies will be given to confirm the results.

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    7
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  • Robust portfolio estimation under skew-normal return processes

    Taniguchi, M, Petkovic, A, Kase, T, DiCiccio, T.J, Monti, A.C

    The European Journal of Finance   iFirst   1 - 22  2012

  • Control variate method for stationary processes

    Tomoyuki Amano, Masanobu Taniguchi

    JOURNAL OF ECONOMETRICS   165 ( 1 ) 20 - 29  2011.11  [Refereed]

     View Summary

    The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE. (C) 2011 Elsevier B.V. All rights reserved.

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  • Cluster Analysis for Stable Processes

    Tsutomu Watanabe, Hiroshi Shiraishi, Masanobu Taniguchi

    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS   39 ( 8-9 ) 1630 - 1642  2010  [Refereed]

     View Summary

    It is known that various financial time series, e.g., daily log returns on a share price, foreign exchange rates, excess bond returns, etc., exhibit heavy-tailed behavior. Recently, discriminant analysis has been applied to financial time series, such as, the problem of credit rating for companies. In this article, we investigate the problem of classifying an -stable linear process into one of two categories with indices 1 and 2, respectively. We propose some discriminant criteria. It is shown that our discriminant statistics are consistent. The misclassification probabilities are also evaluated under contiguous hypotheses. Some numerical studies for an (AR(1)) process are given.

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  • Empirical likelihood approach for non-Gaussian vector stationary processes and its application to minimum contrast estimation

    Ogata, H, Taniguchi, M

    Austral. New Zeal. J. Statist.   52   451 - 468  2010

  • 時系列解析の漸近理論

    谷口 正信

    数学、 岩波   62   50 - 74  2010

  • Local Whittle likelihood estimators and tests for non-Gaussian stationary processes

    Tomohito Naito, Kohei Asai, Tomoyuki Amano, Masanobu Taniguchi

    Statistical Inference for Stochastic Processes   13 ( 3 ) 163 - 174  2010

     View Summary

    In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density fθ (λ) around λ, we propose a local estimator θ̂=θ̂(λ) of θ which maximizes the local Whittle likelihood around λ, and use fθ̂(λ)(λ) as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated by a few simulated numerical examples. © 2010 Springer Science+Business Media B.V.

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  • Discriminant analysis for dynamics of stable processes

    Motoyoshi Nishikawa, Masanobu Taniguchi

    Statistical Methodology   6 ( 1 ) 82 - 96  2009.01

     View Summary

    We consider the problem of classifying an α-stable linear process into two categories described by two hypotheses π1 and π2. These hypotheses are specified by the "normalized power transfer functions" over(f, ̃) (λ) and over(g, ̃) (λ) under π1 and π2, respectively. In this paper, we suggest a classification statistic In (over(f, ̃), over(g, ̃)) based on the normalized power transfer functions. We show that In (over(f, ̃), over(g, ̃)) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as the sample size tends to infinity. When over(g, ̃) (λ) is contiguous to over(f, ̃) (λ), we also evaluate the goodness of fit of In (over(f, ̃), over(g, ̃)) in terms of the misclassification probabilities. Our results have potential applications in various fields, e.g., credit rating in finance, and so on. Several numerical examples will be given. © 2008 Elsevier B.V. All rights reserved.

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  • Cressie-Read power divergence statistics for non-Gaussian stationary processes

    Ogata, H, Taniguchi, M

    Scandinavian J. Statistics   36   141 - 156  2009

  • Classification and similarity analysis of fundamental frequency patterns in infant spoken language acquisition

    Hiroko Kato Solvang, Masanobu Taniguchi, Tomohiro Nakatani, Shigeaki Amano

    Statistical Methodology   5 ( 3 ) 187 - 208  2008.05

     View Summary

    Fundamental frequency (F0) patterns, which indicate the vibration frequency of vocal cords, reflect the developmental changes in infant spoken language. In previous studies of developmental psychology, however, F0 patterns were manually classified into subjectively specified categories. Furthermore, since F0 has sequential missing and indicates a mean nonstationarity, classification that employs subsequent partition and conventional discriminant analysis based on stationary and local stationary processes is considered inadequate. Consequently, we propose a classification method based on discriminant analysis of time series data with mean nonstationarity and sequential missing, and a measurement technique for investigating the configuration similarities for classification. Using our proposed procedures, we analyse a longitudinal database of recorded conversations between infants and parents over a five-year period. Various F0 patterns were automatically classified into appropriate pattern groups, and the classification similarities calculated. These similarities gradually decreased with infant's monthly age until a large change occurred around 20 months. The results suggest that our proposed methods are useful for analysing large-scale data and can contribute to studies of infant spoken language acquisition. © 2007 Elsevier B.V. All rights reserved.

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  • Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets

    Hiroshi Shiraishi, Masanobu Taniguchi

    JOURNAL OF FORECASTING   27 ( 3 ) 193 - 215  2008.04  [Refereed]

     View Summary

    This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators First, it is shown that there are some cases when the asymptotic variance of under non-Gaussianity can be smaller than that under Gaussianity. The result shows that non-Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for (g) over cap to be asymptotically efficient when the return process is Gaussian, which shows that (g) over cap is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one-step-ahead optimal portfolio return by the estimated portfolio based on (g) over cap and examine the mean squares prediction error. Copyright (c) 2008 John Wiley & Sons, Ltd.

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  • Non-regular estimation theory for piecewise continuous spectral densities

    Masanobu Taniguchi

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   118 ( 2 ) 153 - 170  2008.02  [Refereed]

     View Summary

    For a class of Gaussian stationary processes, the spectral density f(theta) (lambda), theta = (tau', eta')', is assumed to be a piecewise continuous function, where tau describes the discontinuity points, and the piecewise spectral forms are smoothly parameterized by eta. Although estimating the parameter theta is a very fundamental problem, there has been no systematic asymptotic estimation theory for this problem. This paper develops the systematic asymptotic estimation theory for piecewise continuous spectra based on the likelihood ratio for contiguous parameters. It is shown that the log-likelihood ratio is not locally asymptotic normal (LAN). Two estimators for theta, i.e., the nnaximurn likelihood estimator (theta) over cap (ML) and the Bayes estimator (theta) over cap (B), are introduced. Then the asymptotic distributions of (theta) over cap (ML) and (theta) over cap (B) are derived and shown to be non-normal. Furthermore we observe that (theta) over cap (B) is asymptotically efficient, but (theta) over cap (ML) is not so. Also various versions of step spectra are considered. (c) 2007 Elsevier B.V. All rights reserved.

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  • Asymptotic efficiency of conditional least squares estimators for ARCH models

    Amano, T, Taniguchi, M

    Statist. Prob. Letters   Vol.78-2   179 - 185  2008

  • Generalized information criteria in model selection for locally stationary processes

    Hirukawa, J, Kato, H, Tamaki, K, Taniguchi, M

    J.Jap. Statist. Soc.   Vol 38-1 ( 1 ) 157 - 171  2008

     View Summary

    The problem of fitting a parametric model of time series with time varying parameters attracts our attention. We evaluate a goodness of time varying spectral models from an information theoretic point of view. We propose model selection criteria for locally stationary processes based on nonlinear functionals of a time varying spectral density without assuming that the true time varying spectral density belongs to the model. Also, we obtain a sufficient condition such that our information criteria coincide with Akaike's information criterion.

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  • Higher order asymptotic option valuation for non-Gaussian dependent returns

    Kenichiro Tamaki, Masanobu Taniguchi

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   137 ( 3 ) 1043 - 1058  2007.03  [Refereed]

     View Summary

    This paper discusses the option pricing problems using statistical series expansion for the price process of an underlying asset. We derive the Edgeworth expansion for the stock log return via extracting dynamics structure of time series. Using this result, we I investigate influences of the non-Gaussianity and the dependency of log return processes for option pricing. Numerical studies show some interesting features of them. (c) 2006 Elsevier B.V. All rights reserved.

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  • Statistical estimation of optimal portfolios for locally stationary returns of assets

    Hiroshi Shiraishi, Masanobu Taniguchi

    International Journal of Theoretical and Applied Finance   10 ( 1 ) 129 - 154  2007.02

     View Summary

    This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them. © World Scientific Publishing Company.

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  • Improved estimation for the autocovariances of a Gaussian stationary process

    Taniguchi, M, Shiraishi, H, Ogata, H

    Statistics   Vol.41-4   269 - 277  2007

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  • Statistical estimation errors of VaR under ARCH returns

    Taniai, H, Taniguchi, M

    J. Statist. Plan. Inf.   To appear  2007

  • James-Stein estimators for time series regression models

    Motohiro Senda, Masanobu Taniguchi

    JOURNAL OF MULTIVARIATE ANALYSIS   97 ( 9 ) 1984 - 1996  2006.10  [Refereed]

     View Summary

    The least squares (I-S) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences. (c) 2006 Elsevier Inc. All rights reserved.

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  • James-Stein estimators for time series regression models

    Motohiro Senda, Masanobu Taniguchi

    JOURNAL OF MULTIVARIATE ANALYSIS   97 ( 9 ) 1984 - 1996  2006.10  [Refereed]

     View Summary

    The least squares (I-S) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences. (c) 2006 Elsevier Inc. All rights reserved.

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    6
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  • Statistical analysis for multiplicatively modulated nonlinear autoregressive model and its applications to electrophysiological signal analysis in humans

    Hiroko Kato, Masanobu Taniguchi, Manabu Honda

    IEEE TRANSACTIONS ON SIGNAL PROCESSING   54 ( 9 ) 3414 - 3425  2006.09  [Refereed]

     View Summary

    Modulating the dynamics of a nonlinear autoregressive model with a radial basis function (RBF) of exogenous variables is known to reduce the prediction error. Here, RBF is a function that decays to zero exponentially if the deviation between the exogenous variables and a center location becomes large. This paper introduces a class of RBF-based multiplicatively modulated nonlinear autoregressive (mmNAR) models. First, we establish the local asymptotic normality (LAN) for vector conditional heteroscedastic autoregressive nonlinear (CHARN) models, which include the mmNAR and many other well-known time-series models as special cases. Asymptotic optimality for estimation and testing is described in terms of LAN properties. The mmNAR model indicates goodness-of-fit for surface electromyograms (EMG) using electrocorticograms (ECoG) as the exogenous variables. Concretely, it is found that the negative potential of the motor cortex forces change in the frequency of EMG, which is reasonable from a physiological point of view. The proposed mmNAR model fitting is both useful and efficient as a signal-processing technique for extracting information on the action potential, which is associated with the postsynaptic potential.

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  • Statistical analysis for multiplicatively modulated nonlinear autoregressive model and its applications to electrophysiological signal analysis in humans

    Hiroko Kato, Masanobu Taniguchi, Manabu Honda

    IEEE TRANSACTIONS ON SIGNAL PROCESSING   54 ( 9 ) 3414 - 3425  2006.09  [Refereed]

     View Summary

    Modulating the dynamics of a nonlinear autoregressive model with a radial basis function (RBF) of exogenous variables is known to reduce the prediction error. Here, RBF is a function that decays to zero exponentially if the deviation between the exogenous variables and a center location becomes large. This paper introduces a class of RBF-based multiplicatively modulated nonlinear autoregressive (mmNAR) models. First, we establish the local asymptotic normality (LAN) for vector conditional heteroscedastic autoregressive nonlinear (CHARN) models, which include the mmNAR and many other well-known time-series models as special cases. Asymptotic optimality for estimation and testing is described in terms of LAN properties. The mmNAR model indicates goodness-of-fit for surface electromyograms (EMG) using electrocorticograms (ECoG) as the exogenous variables. Concretely, it is found that the negative potential of the motor cortex forces change in the frequency of EMG, which is reasonable from a physiological point of view. The proposed mmNAR model fitting is both useful and efficient as a signal-processing technique for extracting information on the action potential, which is associated with the postsynaptic potential.

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    12
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  • Statistical analysis of a class of factor time series models

    M Taniguchi, K Maeda, ML Puri

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   136 ( 7 ) 2367 - 2380  2006.07  [Refereed]

     View Summary

    For a class of factor time series models, which is called a multivariate time series variance component (MTV) models, we consider the problem of testing whether an observed time series belongs to this class. We propose the test statistic, and derive its symptotic null distribution. Asymptotic optimality of the proposed test is discussed in view of the local asymptotic normality. Also, numerical evaluation of the local power illuminates some interesting features of the test. (c) 2005 Elsevier B.V. All rights reserved.

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  • LAN theorem for non-Gaussian locally stationary processes and its applications

    J Hirukawa, M Taniguchi

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   136 ( 3 ) 640 - 688  2006.03  [Refereed]

     View Summary

    For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown. (c) 2004 Elsevier B.V. All rights reserved.

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  • Higher order asymptotic option valuation for non-Gaussian dependent return

    Tamaki, K, Taniguchi, M

    J. Statist. Plan. Inf.    2006

  • Minimum alpha-divergence estimation for arch models

    SA Chandra, M Taniguchi

    JOURNAL OF TIME SERIES ANALYSIS   27 ( 1 ) 19 - 39  2006.01  [Refereed]

     View Summary

    This paper considers a minimum alpha-divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjostheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251-273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445-463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215-234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation.

  • Minimum alpha-divergence estimation for arch models

    SA Chandra, M Taniguchi

    JOURNAL OF TIME SERIES ANALYSIS   27 ( 1 ) 19 - 39  2006.01  [Refereed]

     View Summary

    This paper considers a minimum alpha-divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjostheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251-273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445-463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215-234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation.

  • The Stein-James estimator for short- and long-memory Gaussian processes

    M Taniguchi, J Hirukawa

    BIOMETRIKA   92 ( 3 ) 737 - 746  2005.09  [Refereed]

     View Summary

    We investigate the mean squared error of the Stein-James estimator for the mean when the observations are generated from a Gaussian vector stationary process with dimension greater than two. First, assuming that the process is short-memory, we evaluate the mean squared error, and compare it with that for the sample mean. Then a sufficient condition for the Stein-James estimator to improve upon the sample mean is given in terms of the spectral density matrix around the origin. We repeat the analysis for Gaussian vector long-memory processes. Numerical examples clearly illuminate the Stein-James phenomenon for dependent samples. The results have the potential to improve the usual trend estimator in time series regression models.

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  • Statistical analysis of a class of factor time series models

    Taniguchi, M, Maeda, K, Puri, M.L

    J. Stat. Plan. Inf. to appear    2005

  • The Stein-James estimator for short- and long- memory Gaussian processes

    Taniguchi, M, Hirukawa, J

    Biometrika, to appear    2005

  • LAN theorem for nonGaussian locally stationary processes and its applications

    Hirukawa, J, Taniguchi, M

    J. Stat. Plan. Inf. to appear    2005

  • Discriminant analysis for time series

    Taniguchi, M

    J.Jap. Statist. Soc. ( in Japanese)    2005

  • Discriminant analysis for time series

    Taniguchi, M

    J. Jap. Statist. Soc. ( Japanese)   35 ( 1 ) 71 - 79  2005

  • Asymptotic theory for ARCH-M models

    Lee, S, Taniguchi, M

    Statistica Sinica   15   215 - 234  2004

  • Asymptotic theory for ARCH-SM models

    Lee, S, Taniguchi, M

    Statistica Sinica   15   215 - 234  2004

  • Taniguchi, M. Recent developments in statistical asymptotic theory for time series analysis.~

    Taniguchi, M

    応用数理   14 ( 1 ) 13 - 23  2004

    Authorship:Lead author

     View Summary

    This paper reviews statistical asymptotic theory for time series. The asymptotic optimality of inference and testing is described in terms of the local asymptotic normality. The results have been applied to financial engineering, biomedical sciences and econometrics etc.

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Books and Other Publications

  • Optimal Statistical Inference in Financial Engineering

    Taniguchi, M, Hirukwa, J, Tamaki, K

    Chapman & Hall  2008 ISBN: 1584885912

  • 数理統計・時系列・金融工学

    谷口 正信

    朝倉  2005

Research Projects

  • Introduction of general causality to various observations and the innovation for its optimal statistical inference

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2018.06
    -
    2023.03
     

  • Theory for quantile regression inference of time series and its applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2015.04
    -
    2019.03
     

    Taniguchi Masanobu, Hallin Marc, Monti Anna Clara

     View Summary

    (1)We introduced a quantile regression statistic to classify time series data into a certain category. Results show that the misclassification probability of the discriminant statistic converges to zero as the sample size tends to infinity. We applied the proposed method in quantile autoregression to a dataset of the monthly mean maximum temperature at Melbourne.The findings illuminate interesting features of climate change and allow us to check the change at each quantile of the innovation distribution.(2)We considered minimax interpolation and extrapolation problems in Lp for stationary processes. We gave two conditions to find the minimax interpolator and extrapolator in the general framework under the Lp-norm. We showed that there exist minimax interpolator and extrapolator for the class of epsilon contaminated spectral densities.The results (1) and (2) open a new methodology for time serires analysis based on quantile informations for probability and spectral distributions

  • 時系列解析における分位点回帰推測論の構築とその応用

    科学研究費助成事業(早稲田大学)  科学研究費助成事業(基盤研究(A))

    Project Year :

    2015
    -
    2018
     

  • Shrinkage Estimation Theory for Unbiased Estimators of Dependent Observations

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2014.04
    -
    2017.03
     

    Taniguchi Masanobu

     View Summary

    Introducing a curved probability model,which includes a class of very general nonlinear time series models,we proposed a shrinkage estimator for unknown parameter of the curved probability models. Then we developed the third-order asymptotic estimation theory for the estimator, and provided a sufficient condition for the shrinkage estimator to improve the usualestimators. The results can be applied to the problem of portfolio coefficient estimation. Because the results are very general, we can apply them to a variety of statistical observations generated by multivariate financial time series, multivariate time series regression models and usual mulitivariate models

  • Asymmetric and nonlinear statistical theory and its applications to economics and bioscience

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2011.04
    -
    2015.03
     

    TANIGUCHI Masanobu, YONEMOTO Kouji, HIRUKAWA Junichi, TAKAGI Yoshiji, HOSHINO Nobuaki, WANG Jin FANG, LIU Qing FENG, NAITO Kanta, SEKIYA Yuri, MATSUDA Shinichi, AKAHIRA Masafumi, TAKEMURA Akimichi, NISHIYAMA Yoshihiko, KANO Yutaka, AMANO Tomoyuki

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    We investigated a class of very general stochastic processes with nonlinear dynamics and asymmetric innovation distributions, which can be applied to a varitety of fields e.g., economics, finance, bionics, natural phenomenon etc., as a paradigm model. For them we developed the optimal inference based on LAN, and the empirical likelihood method to a class of stable processes. Shrinked estimation theory has been developed for stochastic processes. The theoretical results have been applied to estimation of portfolios, and the problem of causality. From the applications of the theoretical results, we have got some interesting feedback to mathematical theory. Also, in the process of research, we have raised young researchers

  • Developments of mathematical statistics through computational algebraic methods

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2010.04
    -
    2014.03
     

    TAKEMURA Akimichi, AOKI Satoshi, IWASAKI Manabu, EGUCHI Shinto, OHSUGI Hidefumi, KAMIYA Hidehiko, KURIKI Satoshi, KOMAKI Fumiyasu, SAKATA Toshio, TANIGUCHI Masanobu, HARA Hisayuki, HIBI Takayuki, YOSHIZOE Yasuto

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    In this project we obtained many important results. The most notable one is the success of the second Institute of Mathematical Statistics Pacific Rim Meeting, held in Tsukuba City during July 1-4 of 2012. The principal investigator of this project was responsible for this important conference in mathematical statistics.Also the principal investigator with Satoshi Aoki and Hisayuki Hara published "Markov bases in Algebraic Statistics" from Springer in 2012

  • 共同研究:金融数理および年金数理研究

    Project Year :

    2011
    -
     
     

  • Theory and Applications for Mathematical Methods in Statistical Science

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2007
    -
    2010
     

    TANIGUCHI Masanobu, YOSHIDA Nakahiro, OCHI Yoshimichi, YAO Feng, WAKAKI Hirofumi, KAKIZAWA Yoshihide, JIMBO Masakazu, MAESONO Nobuhiko, ANO Yutaka, HIRUKAWA Junichi, SHIMIZU Kunio, KONDO Masao, UNO Chikara, MIYATA Yoichi, TAKADA Yoshikazu, NOMAKUCHI Kentaro, KURIKI Shinji, KATO Takeshi, AKAHIRA Masafumi, TAKEMURA Akimichi, KONISHI Sadanori, TAKAHASHI Daisuke, MAEKAWA Koichi, SUZUKI Takeru, NISHII Ryuei, SASABUCHI Yoichi, AKI Shigeo, KURIKI Satoshi, AOSHIMA Makoto, TAMAKI Kenichiro, SHIRAISHI Hiroshi, SHIRAHATA Shingo, SHIOHAMA Takayuki

     View Summary

    Mathematical models that describe random phenomena depending on past, present and future are called stochastic processes. In this research we established statistically optimal estimation theory for general stochastic processes, and applied the theoretical results to various fields, e.g., finance, economics, medical sciences, engineering and environment etc., yielding a lot of contributions. We performed the research with many foreign researchers as well as domestic ones, and developed young researchers.

  • Semiparametric Econometrics based on moment conditions-theory and applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2006
    -
    2009
     

    NISHIYAMA Yoshihiko, YAJIMA Yoshihiro, TANIZAKI Hisashi, HITOMI Kotaro, NAGAI Keiji, TANIGUCHI Masanobu, ICHIMURA Hidehiko, OYA Kosuke

     View Summary

    Econometricians have used nonparametric and semiparametric techniques to investigate economic data for empirical justification of economic theories and policy evaluation since 1990s. This is still a relatively new topic in this field. With the advances of IT technology, micro data and panel data are getting accessible more easily and the need for such modeling and statistical methods is becoming more and more important. We have developed such methods aaplicable in econometric

  • 局外母数をもつ時系列回帰モデルのセミパラメトリックな高次漸近理論

    科学研究費助成事業(早稲田大学)  科学研究費助成事業(萌芽研究)

    Project Year :

    2005
    -
    2007
     

     View Summary

    セミパラメトリックな高次推定では、時系列回帰モデルにおいて回帰係数の推定に残差スペクトルの非母数的推定量に基づいたHannan推定量の高次のasymptoticsを明らかにした。結果として通常の高次セミパラメトリック推定では、関与の推定量の分布の高次項は非母数推定量のカーネル関数に依存するが、Hannan推定量は、2次までの近似項がカーネル関数に依存しないという結論を得た。これは、従来のこの分野の結果と本質的に異なり、Hannan推定量の特殊性を示している。
    非正則モデルの統計解析においては、定常過程のスペクトル密度関数が不連続点を持つ場合のスペクトルのダイナミクス母数と不連続周波点の推測を行った。この結果、不連続周波点の推定量のasymptoticsは従来のそれと異なり、また漸近有効性の面でも、最尤推定量が一般に漸近有効とはならないで、Bayes推定量が漸近有効となることが判明し、従来の推定論と大きく異なることが判明した。
    正規過程の共分散関数の推定において、従来は標本共分散を用いるが、標本共分散関数で縮小、拡大項をつけた推定量を提案し、このasymptoticsを明らかにした。従来の標本共分散と新しい推定量は、3次の漸近理論の意味で、差があり、この差を2乗誤差で評価した。自己回帰モデルなどでは、単位根に近いほど、新しい推定量が従来のを改善していることが判明した。
    その他、局所定常時系列の判別解析で、理論的結果を得、その応用でも種々の結果を得た。

  • Statistical inference for discrete patterns in dependent sequences

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2002
    -
    2005
     

    AKI Sigeo

     View Summary

    We have studied the distributions of numbers of occurrences of discrete patterns and waiting time distributions for them in various dependent sequences. The following results have been derived.1. By using a combinatorial method it is shown that for every finite pattern, the distribution of the waiting time for the reversed pattern coincides with that of the waiting time for the original pattern in a multi-state dependent sequence with a certain type of exchangeability. The corresponding results for the waiting time for the r-th occurrence of the pattern, and for the number of occurrences of a specified pattern in n trials are also studied. Illustrative examples based on urn models are also given.2. Several waiting time random variables for a duplication within a memory window of size k in a sequence of {1,2,...,m}-valued random variables are investigated. The exact distributions of the waiting time random variables are derived by the method of conditional probability generating functions. In particular, the exact distribution of the waiting time for the first k-match is obtained when the underlying sequence is generated by higher order Markov dependent trials. Examples for numerical calculations are also given.3. We consider waiting time problems for two-dimensional pattern in a sequence of i.i.d. random vectors each of whose entries is 0 or 1. A general method for obtaining the exact distribution of the waiting time for the first occurrence of the pattern in the sequence is presented. The method is an extension of the method of conditional probability generating functions and it is very suitable for computations with computer algebra systems as well as usual numerical computations. Computational results applied to computation of exact system reliability are also given.4. Let k and m be positive integers with k>m. The probability generating function of the waiting time for the first occurrence of consecutive k successes in a sequence of m-th order Markov dependent trials is given as a function of the conditional probability generating functions of the waiting time for the first occurrence of consecutive m successes. This provides an efficient algorithm for obtaining the probability generating function when k is large. In particular, in the case of independent trials a simple relationship between the geometric distribution of order k and the geometric distribution of order k-1 is obtained.5. Various new distributions related to runs and patterns in dependent sequences are obtained by using the stepwise smoothing formula for conditional expectations

  • A STUDY ON STATISTICAL INFERENCE OF STOCHASTIC PROCESS AND ITS ROBUSTNESS

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2002
    -
    2004
     

    INAGAKI Nobuo, SHIRAHATA Shingo, KANO Yutaka, KUMAGAI Etsuo, AKI Shigeo

     View Summary

    Our aim of this study is to investigate the statistical inference of stochastic processes by their likelihood functions, especially for "exponential" stochastic processes and furthermore, to investigate the robust statistical inference for observations with additive outliers. The important mathematical structure of statistical inference is discussed by using the statistical informations in exponential stochastic processes.Our plan of this study is as follows :(1) We study the likelihood function of parametric models of stochastic process, especially exponential stochastic processes, and their statistical informations by the stochastic integral and Ito's formula.(2) We investigate 'the relationship between the statistical curvature and the information loss.(3) We study asymptotic methods in nonparametric and semi-parametric models and evaluates the performance of them by simulation experiments.(4) We study the first occurrence time of run and pattern in dependent sequence of bivariate observations.Our results of this research project are as follows :(1) We published the revise of "Mathematical Statistics" (in Japanese).(2) We write a paper "Exact information loss in multivariate gamma distribution" at Scientiae Mathematicae Japonicae (SCMJ) (2005).(3) We published a paper about a selection of models (2005) in press.(4) We write several papers about distributions of runs and patterns in dependent processes

  • A STUDY ON ASYMPTOTIC STRUCTURE OF STATISTICAL INFERENCE FOR PARAMETRIC MODELS OF STOCHASTIC PROCESS

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1999
    -
    2001
     

    INAGAKI Nobuo, TANIGUCHI Masanobu, ISOGAI Takafufumi, SHIRAHATA Shingo, KUMAGAI Etsuo, AKI Shigeo

     View Summary

    AIM : Our aim of this study is to investigate the mathematical structure of statistical inference by the asymptotic behavior of likelihood functions of parametric models of stochastic process and especially, to investigate the likelihood functions of "exponential"stochastic processes and their asymptotic properties. The important mathematical structure of statistical inference is discussed by using asymptotic properties of the statistical informations in exponential stochastic processes.PLAN : Our plan of this study is as follows: (1) INAGAKI studies the likelihood function of parametric models of stochastic process, especially exponential stochastic processes, and their statistical informations by the stochastic integral and Ito's formula. (2) INAGAKI and KUMAGAI investigate the asymptotic relationship between the statistical curvature and the information loss by which they give the charicterization of Efron's parametrization. (3) SHIRAHATA studies the asymptotic methods in nonparametric and semi-parametric models and evaluates the performance of them by simulation experiments. (4) TANIGUCHI investigates the robustness in the time series analysis. (5) AKI studies the first occurrence time of run and pattern in dependent sequence, such as Markov dependent trials and sampling from urn models.RESULTS : Our results of this research project are as follows: (1) INAGAKI published a book "FOUNDAMENTALS OF STATISTICS" (in Japanese) with other two coauthors. (2) INGAKI and KUMAGAI write a paper "On Efron's parametrization" at Australian & New Zealand Journal os Statistics (2002) (in press) with another coauthor. (3) SHIRAHATA published a paper about the response ratios of each quation in sampling quationnaire. (4) TANIGUCHI writes a paper about the robustness in time series analysis. TANIGUCH and KAKIZAWA published a book "Asymptotic Theory of Statistical Inference for Time Series" Springer, Verlag, New York. (5) AKI writes several papers about distributions of runs and patterns in dependent processes

  • Researches on the Non-Regular Inference Theory and the Concepts of the Amounts of Information

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1998
    -
    2001
     

    AKAHIRA Masafumi, YOSHIDA Nakahiro, SHIRAISHI Takaaki, FUJIKOSHI Yasunori, KOIKE Ken-ichi, AOSHIMA Makoto

     View Summary

    The statistical investigation on various themes was done as follows.(l)0n the statistical inference and its related topics, the inferential procedures were proposed and interesting results on the application were obtained.(2)0n the statistical non-regular theory, the properties of estimators were discussed, and new knowledges of the characterization of non-regular distributions were obtained.(3)0n the theory of inference and its information theoretic viewpoint, the structure of inference was clarified through amounts of information, and its relation to the theory of information was well investigated.(4)0n the fundamental theory to analyze the statistical model with prior informations and its applications, the optimality of inferential procedures was considered from the Bayesian point of view, and the results on possibility of the application to practical problems were obtained.(5)The space between multivariate analysis and time series was investigated in details, and new results on the comparison of inferential procedures were given.(6)0n the combinatoric design and its applications, the construction of experimental design was proposed and assessed.(7)0n the economic time series and mathematical finance, the construction of the fundamental theory of statistical inference was tried and its usefulness is investigated.(8)0n the multivariate analysis, the linear and non-linear models were discussed, and new results on the inference were obtained in the non-regular case which was regarded as a difficult one.(9)The theoretical fundamentals and its applications were well investigated from the viewpoint of sequential analysis, and new results on the inferential procedures were obtained in the case of non-regular distributions.(10)0n the statistical and mathematical anakysis, new results on the efficiency of estimation and test procedures were given.In addition to the above, the results on the statistical modeling and inference, the spatial statistics, the recent computer-assisted type inference and its applications and others were also obtained. Many symposiums on the above were held and active discussions and mutual exchanges of informations were also done. Their results were summarized as a book of about 800 pages

  • Theory and application of information extraction in mathematical statistics

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1996
    -
    1997
     

    TAGURI Masaaki, SUZUKI Takeru, KANAZAWA Mitsuyo, TARUMI Tomoyuki, KUSHIMOTO Shigeru, YANAGAWA Takashi

     View Summary

    In this research, we investigated the theory of information extraction in mathematical statistics and applied the results to various kinds of practical data-set. 11 special topics were selected and research sympojiums were held on each topic. As a result, new theories and methodologies were developed and useful knowledges were obtained in many practical fields. Statistical software were also constructed. Through discussions in sympojiums and meetings, further problems were pointed out. Main results obtained in 11 sympojiums were as follows :(1) Development of the theories and methodologies for analyzing complicated nonlinear data and investigation on the limit in practical use.(2) Research of descriptive statistics and statistical inference on multivariate analysis, and the understanding of their discrepancy.(3) Development of optimization theories in mathematical programming and model construction for applying the results to practical problems.(4) Investigation on asymptotic theory, large deviation theory, model selection in time series analysis and their application.(5) Investigation on the theories and methodologies of sample sizes in sequential analysis required to carry out efficient statistical inference.(6) Investigation on probability distributions and sampling distributions concerning various statistical models.(7) Investigation on combinatorial mathematics, integral conditions and optimization in statistical model construction and inference.(8) Development of the theories on computer-intensive statistical methods and construction of useful statistical software.(9) Development of statistical asymptotic theory and construction of the computer-intensive algorithms.(10) Investigation on statistical inference concerning multivariate model, stochastic process model, time siries model and Baysian model.(11) Construction of good estimators and joint confidence intervals, and investigation on their properties

  • Discriminant analysis for time series

    Project Year :

    1996
     
     
     

  • LAN approach for time series

    Project Year :

    1996
     
     
     

  • 非指数型分布族における統計的高次漸近理論の研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1995
     
     
     

     View Summary

    (1)検定論における高次漸近理論を非指数族及び時条列解析を含む形でまとめることが出来た.具体的には,十分広い検定統計量のクラスを定義して,このクラスに属する検定の2次及び3次のlocrl pouerの評価式を与え,これより2次漸近不偏にすれば,このクラスの検定の2次ローカルパワーは一致し,3次のローカル,パワーは統計的曲率がゼロでないかぎり,一様な結果が得られぬことが判明した.また非指数型分布族及び時条列モデルを含む形で検定のバ-トレット調整が可能であるための十分条件を与えた.さらに同様の状況で,スチューデンタイズド統計量の2次のEdgwerth展開にdualitgがあることを示した.このことはスチューデンタイズド統計量と双対幾何が溶接に関連していることを意味しており,今後のさらなる課題である.
    (2)時条列解析における非母数的アプローチは理論面からも応用面からも必要とされている.以下の結果が得られた.非正規ベクトル値過程のスペクトル密度行列のran-linearな関数の積分量に関する検定問題で,検定統計量をノンパラメトリックなスペクトル密度行列の指定量のran-linearな関数の積分に基づいて定義して,この検定統計量の仮説とローカルな対立仮説のもとでの漸近分布を求めた.さらにこれらの漸近分布は非正規性の影響があらわれる.この影響が消えるための十分条件を与えた.
    以上の検定問題は極めて応用がひろく,経済時条列の因果性に関する検定問題,スペクトル密度行列の固有値に関する検定問題,等種々の応用があることを示した.また地震波の判別解析にも用いることが出来、よい応用結果を得つつある.

  • ノンパラメトリックな回帰分析の研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1995
     
     
     

     View Summary

    ノンパラメトリック回帰分析では目的変数の説明変数への関連の仕方に対する仮定が緩い。その中で、本研究では説明変数の一部xには線形模型、残りのtに対しては関連の仕方が未知と仮定したセミパラメトリック回帰分析、すなわちy=βx+g(t)なるモデルを扱った。ノンパラメトリック回帰分析では偏差平方和と連続性に対する罰則を加えた値を最小にすることによって推定量が導かれ、スプライン関数を用いて構成される。また偏差平方和と罰則のバランスをとる平滑化パラメータがある。標準的推定量は部分平滑化法であるが、回帰パラメータの推定量に偏りが発生し、それを小さくするために、tに従属する部分を除いて考える偏回帰推定量や連続性への罰則をxのtに関連する部分にも付ける2段階平滑化推定量が提案されてきた。本研究では、これらの3方式で漸近的には正規性・不偏性が成立し、その偏りのオーダーもすべて一致することを示した。さらに、偏りをより詳細に検討し、偏回帰推定量の偏りは実際に部分平滑化推定量より小さくなることが期待できることを示した。また2段階平滑化推定量には2つの平滑化パラメータが必要であるが、うまく選択できれば部分平滑化推定量より偏りを小さくできることを示した。さらに、うまく選択できれば部分平滑化推定量より偏りを小さくできることを示した。さらにこれらの理論的・漸近的結果を確認するためのコンピュータ・シミュレーションを行った。部分平滑化推定量では想定するg(t)によって偏りは大きく変化する。一方、偏回帰推定量でもそれと同じ傾向がある強くない。2段階平滑化推定では確かに平滑化パラメータをうまく選べば偏りを小さくできるが、実際にそれらを求めるのは難しいことが分かった。さらに最適な平滑化パラメータを求めるアルゴリズムとして交差確認法が一般に推奨されるが、偏りに対してはは必ずしも良い結果を与えるとは限らないことが示された。これらの結果はとりまとめて現在学術雑誌に投稿中である。

  • 可逆マルコフ過程の関数解析的研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1994
     
     
     

     View Summary

    対称マルコフ過程の加法的汎関数の分解定理の精密化とその応用を図るという研究目的に沿った申請書の研究計画・方法に従って研究を進めた結果以下の研究業績を得ることが出来た。
    代表者福島は分担者竹田および熊本大学の大島教授と共に、共著の著書(1994年発刊)において上記分解定理のみならず、その局所的な場合への拡張及び推移確率が絶対連続な場合における精密化についての基礎理論を展開している。特に精密化に関してはいくつかの十分条件が与えられているが、福島はこの一般論を徹底して進め、加法的汎関数u(X_t)-u(X_o)のマルチンゲ-ル部分M_tとエネルギー零の部分N_tとの和としてのstrictな分解が成立するための関数uに対する必要十分条件やN_tが有界変動になるためのuに対する必要十分条件を求めることに成功し、更にN_tのstrictな意味での台とuのスペクトルの関係を明らかにした。福島はこの一般論を山口大学の富崎教授と共同で応用して境界がヘルダー連続性しか持たないR^d上の領域に対し、ヘルダー指数がd/(d-1)より大きい時にはその領域上の反射壁ブラウン運動はスカラホ-ド分解を許容することを証明した。実はdの如何にかかわらずヘルダー指数が1/2より大きいときにこれは正しいという予想を持ち目下その証明に取り組んでいる。
    分担者竹田は上記共著の著書で展開された対称マルコフ過程の乗法的汎関数による変換とデイリクレ形式の変換の関係に関する基礎理論の発展に取り組んでいる。特に上述の加法的汎関数の分解定理の精密化を用いることによって優マルチンゲ-ル的な乗法的汎関数による変換論の精密化に成功している。
    また尾角は数理物理的な可解格子模型にたいして、稲垣、谷口、安芸は統計的モデルに対してそれぞれ汎関数の分解定理の有効性を示す研究を着実に進めた。

  • Nonparametric approach for time series

    Project Year :

    1993
     
     
     

  • 確率過程における母数モデルと統計的推測の研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1993
     
     
     

     View Summary

    1.研究目的:近年注目されている確率過程の母数モデルにおける統計的推測の研究を新しい数理科学の方法を導入して行うことを目的とした.経済時系列モデル;寿命解析における点過程積強度モデル;数理地震学におけるストレス解放モデルなどの数理モデルに基づき,モデル選択・モデル適合という統計推測決定の総合された理論の展開を行う.統計的情報量・数理幾何学・数理代数学など数理科学の新しい概念や解析方法を情報理論や幾何学代数学の専門家が協力して研究し,数理モデルの開発やその理論と応用の整合を研究を行った.
    2.研究計画:各研究分担者は下記の4つのテーマの役割分担に対する研究班:
    (1)確率過程の母数モデルの統計的推測理論の研究(稲垣,安芸,白旗)
    (2)数理幾何学・数理代数学による数理モデルの構造の研究(伊達,尾角,三木)
    (3)確率過程の母数モデルの研究(福島,竹田)
    (4)統計的決定理論の有効性の研究(石井,谷口)
    を組織し,新しい数理モデルと統計的推測決定理論によって現象の数学的構造を解明する研究を行った.現象の推測・決定に有効か実行性があるかをパソコンやワークステイションを駆使してシミュレーション実験によって検討した.
    3.研究成果:(1)稲垣は確率点過程におけるストレス解放モデルに関して研究を行い,安芸は成功連の長さの分布の研究を行い,白旗は一様分布の特性付けの研究をした.(2)伊達,尾角,三木はアフィン代数に関するスピンモデルのスペクトルの研究を行った.(3)福島,竹田はディリクレ形式の加法フラクタルと一般シュレジンジャー作用素の研究を行った.(4)石井,谷口は時系列解析における判別解析,ノンパラメトリック解析を行った.これらの研究は論文として公表した.

  • Nonparametric approach for time series

    Project Year :

    1993
     
     
     

  • 確率過程の関数解析的研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1992
     
     
     

     View Summary

    確率諸過程の関数解析的研究という目的に沿った申請書記述の研究計画・方法に従って研究を進めた結果以下の研究実績を得ることが出来た。
    代表者福島は正則Dirichlet形式にHunt過程を容量0の集合を除いて一意的に構成するという20年前の方法を拡張して、(r,p)-容量0というもっと精細な集合を除いての構成をある擬微分作用素の族に対して実行した。福島と分担者竹田は熊本大学の大島洋一氏との平成5年出版予定の共著の著書に於いてDirichlet形式とマルコフ過程の関係についての基礎理論を更に充実させ、特にextended Dirichlet spaceの理論、マルコフ過程のtime changeとの対応理論、対称作用素のマルコフ拡大の理論をほぼ完成させて載せることができた。
    福島と分担者島はSierpiski gasketという代表的なフラクタル集合上で最近導入されたラプラス作用素に対してその固有値、スペクトルを精細に調べいくつかの通常と異なるwildな性質を発見した。更により一般なフラクタル集合であるnested fractal上のラプラス作用素に対してもそのスペクトル分布関数の原点の近くでの増大度にフラクタルのスペクトル次元と呼ばれる量が関係していることを福島が見いだし、島はランダムなポテンシャルを持つ対応するシュレージンガー作用素についてもそのスペクトル分布関数のLifchitz tailとしてやはりフラクタル次元が現れることを発見した。これらの研究に於いてDirichlet形式論が極めて有効な働きをすることが確認され今やそれはフラクタル集合上の解析学や拡散過程の研究に欠かせない枠組みとなっている。
    また伊達は数理物理学的な可解格子模型に対して、谷口、安芸は統計学的モデルに対して、それぞれ2次形式やエネルギー概念の有効性を示す研究を着実に押し進めた。

  • Research on Test and Estimate of Distribution Function and its Functionals

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1991
    -
    1992
     

    SHIRAHATA Shingo, CHU In-sun, AKI Shigeo, TANIGUCHI Masanobu, ISOGAI Takafumi

     View Summary

    Distribution function and its functionals play important roles in statistical inferences. In parametric frame works, the likelihood is represented by density functions. In nonparametric theory, several hypotheses are given by distribution functions. The aim of this research project is to develop theory and method on test and estimate of distribution function and its functionals. The head investigator and the investigators singly or jointly obtained the following results.
    1. In the estimate of distribution function, the kernel estimators are better than the empirical distribution function in the sense of integrated mean squared error. In our work, the superiority of the kernel estimator is shown to be not true in the sense of integrated squared error. Hence, we recommend to use kernel estimator if we adhere the continuity, and to use empirical distribution function if otherwise. 2. We must give the smoothing parameter in the kernel estimators. In order to select the parameter, we must estimate the errors. It is shown that the bootstrap method is very useful in the estimate of the errors. 3. The usual confidence band of distribution function is based on the supremum of the absolute deviation. However, the band is not accurate for extreme points. A new confidence band is given in order to recover the defect of the usual method. 4. Goodness of fit tests based on graphical representation of data and a characterization of distribut ions are proposed. 5. The second order and the third order efficiency of statistics in time series and non-linear regression models are derived. 6. Some extensions of binomial distribution of order k and negative binomial distribution of order k are considered. Moment generating functions and variances of waiting time occurred in two-state Markov chain are derived.

  • 数理モデルの代数的構造の研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1991
     
     
     

     View Summary

    量子展開環Uq(oy)において、qがlの巾根である場合には、この場合に特有な有限次元表現(ここでは巡回表現と呼ぶ)がある。その主たる特徴の一つは、通常の最高ウエイト表現の場合には異なり、表現が連続パラメ-タに依ることである。Uq(oyl(n.〓))の場合に、最大個数のパラメ-タを含む表現を具体的に構成した。また、量子展開環が余可換でないことから、二つの表現のテンソル積表現の成分を入れ換えたものは、一般にはもとの表現とは同型でない。Uq(oyl(n.〓))の最低次元の巡回表現の場合に、これらが同型となるためにパラメ-タの間になりたつべき代数的関係式の十分条件を求め、それらの表現の間の繋絡作用素を構成した。この作用素の行列成分をボルツマン重率として指定することにより種数が1より大きい代数曲線と関係する可解格子模型の一つの族が構成できた。また、このようにして得られる可解格子模型と関係する結び目、絡み糸の不変量も構成した。Uq(A^<(2)>_2)の最低次元巡回表現の場合の繋絡作用素も構成した。
    その他、可解格子模型の統計物理的量の計算の方向の研究も進行中である。研究分担者はそれぞれの分担分野において次のような成果を挙げた。
    フラクタル集合上のラプラス作用素に関するスペクトル解析及びそれに対応する拡散過程の再帰性について。完備リ-マン多様体上のブラウン運動の非爆発のための十分条件の確率論的導出。一般シュレディンガ-作用素の最大自己共役拡大の存在について。推定関数の漸近バイアス性の推定量への伝播について(回帰分析におけるリッジ推定量の適用範囲について)。ストレスリリ-ス確率過程モデルにおけるレベルの推定問題について。推定検定及び時系列解析における高次の漸近分布の研究。二値独立同分布確率変数列におけるLingの二項、負二項分布の性質について。離散確率変数列の待時間問題について。

  • Researches on Statistical Inference and Its Applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1990
    -
    1991
     

    AKAHIRA Masafumi, KUWADA Masahide, KUBOKI Hisataka, NAKAI Toru, TAKADA Yoshikazu, TANIGUCHI Masanobu

     View Summary

    Recently, the statistical inference and its applications have been extensively developed. The purpose of this research is to investigate various problems on the statistical inference from the viewpointsof small sample theory and large sample one and to obtain the results on the inference. In particular, we chose 10 important topics on the inference and made up a group per topic. which consists of the investigators and others. We also drew up a plan to hold meetings on the topics and proceeded with the study collectively to contribute to the field of statistics. The topics are the following : (1) Optimality in estimation and testing hypotheses (2) Theory of time'series anlysis and its applications, (3) Amount of information and statistical inference, (4) Statistical inference on experimental designs and its applications, (5) Theory of statistical multivariate analysis and its applications, (6) Modeling and analysis in mathematical programming, (7) Statistical graphics and its applications, (8) Theory of sampling and resampling and its applications, (9) Asymptotic theory of statistics and its applications, (10) Testing statistical hypothesis and related topics.
    The meeting on each topic was held with many attendants, and there many new results were presented with active discussions. It seemed to be very meaningful. The results on the topics were completed as a report of the study.
    We believe that these results largely contribute to the theory of statistical inference and its applications. Their further developments are expected.

  • 統計的推測に関連する最適化理論の研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1990
     
     
     

     View Summary

    研究計画に従って,研究代表者および研究分担者が研究を進めた結果,得られた成果を,進行中のものも含めて報告する.
    1.最適化の一般理論を統計的推測に応用する場面においては,測度の空間(確率過程のように関数空間上の測度も含む),統計量の空間,検定関数の空間などの無限次元線形空間における最適化理論が登場する.これについて,研究代表者らは,以前から,数理統計学に必要な範囲で一般論を展開し,統計的諸問題への応用を試みたが,もっと応用範囲を広げるためには,より一般の線形位相空間における最適化理論を論じる必要がある.研究代表者は,以前よりさらに一般な形の最適化理論を定式化し,最適解の特徴づけや双対定理についての包括的な理論を得ており,近く論文としてまとめる予定である.
    2.統計的推測の対象が時間に従って変動する確率事象の場合,確率過程に関する母数推定や検定の問題が生じる.また,動的計画法や遂次決定理論を扱うには,その基礎として確率過程に関する統計的推測の問題は欠くことのできないものである.確率過程の推測を研究する分担者は,拡散過程や点過程に関する統計的諸問題の考察を通じて最適化の諸問題を提起した.また,時系列解析に関する分担者は,母数推測の最適性を高次の有効性の立場から論じた.
    3.確率過程に関する分担者は,上記2で提起されたことの基礎となる確率過程についての理論的研究を行った.
    4.数理モデル担当の分担者は,本研究課題と関連の深い統計力学に関する数理モデル,とくに可解格子模型の研究を通じて,本研究に協力貢献した.

  • Uー統計量の応用的研究

    科学研究費助成事業(大阪大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1990
     
     
     

     View Summary

    1.Uー統計量は最良不偏推定量であり、弱い条件の下で漸近正規性が成立する,という理論的最適性を持つ・しかしながら,その計算量の大きさのために次数の大きい場合は実用的とはあまり見なされなかった.また区間推定を行なうには,その分散を推定する必要があるが,実用的な分散推定量は知られていなかった.本研究の目的はUー統計量のこれらの難点を克服することにあった.2.計算量を小さくする問題は,2標本問題において実用的な多くの場合に適用できるようこれまでの研究を整理し,さらに一般な場合への拡張を試みているが,理論的にはまだはっきりしない.3.Uー統計量の分散の推定では,分散をさらに高次の核関数を持つUー統計量で推定する方法(U法),ジャックナイフ法,ブ-ツトラップ法およびそれらを不偏となるように変換した方法を多くのUー統計量について計算機シミュレ-ションで比較し,U法とブ-ツトラップ法が総合的に優れていることを示した.さらに,最も実用的なUー統計量であるマン・ホイットニ-統計量の場合にはU法が最良との結論に達した.これらの結果は現在投稿中または投稿準備中である.その他の2標本Uー統計量の場合についても現在数値計算を行なっている.4.分布関数を推定する場合に,平均2乗誤差の意味では複雑な核型推定量が良いと証明されているが,2乗誤差では単純な経験分布関数との違いは小さく,本質的には差がないことを示した.これらの証明にはUー統計量の特質を用いており,結果は現在投稿中である.5.研究分担者の研究は以下のとおり.(1)稲垣・高木はUー統計量を含む推定関数の漸近理論を研究し,学会で講演予定.(2)松尾は一般化線形模型をUー統計量の立場からまとめている.(3)谷口は時系列への応用を研究し,テクニカル・レポ-トにまとめ,学会で講演予定.論文は投稿準備中である.

  • A Study on Asymptotic Methods for Statistical Inference

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1989
    -
    1990
     

    INAGAKI Nobuo, TANIGUCHI Masanobu, SHIRAHATA Shingo, DATE Etsurou, FUKUSHIMA Masatoshi, ISII Keiiti

     View Summary

    AIM : Our aim of this study is to investigate the mathematical structure of estimation and test in statistical inference by the asymptotic behavior of likelihood function of parametric models, and especially, to investigate the asymptotic structure of new parametric models in stochastic process. In the case of nonparametric models, we treat estimators and test statistics written down as functionals of empirical distribution function and investigate those asymptotic properties by properties of integrals of Wiener measure.
    PLAN : Our plan of this study is as follows : (1) INAGAKI studies the relationship between the differentiability and asymptotic expansion of the likelihood function, especially, in the parametric models of stochastic processes. (2) INAGAKI and MATSUO study the roles of link functions and quasilikelihoods in the general linear regression model, which is useful in Application Statistics.
    (3) SHIRAHATA studies the asymptotic methods in nonparametric models and evaluates the performance of them by simulation experiments. (4) TANIGUCHI investigates the robustness in the time series analysis, which is recently developed. (5) ISII, FUKUSHIMA and DATE study the mathematical foundation of the asymptotic theory of statistical inference.
    RESULTS : Our results of this research project are as follows : (1) INAGAKI published a book "STATISTICAL MATHEMATICS" (in Japanese) in section "LIKELIHOOD ANALYSIS" of which the role of likelihood function is expressed for the asymptotic theory of estimation and test. Also, he read a paper "simple self-correcting point processes with several levels" at the annual meeting (1990) of the MATHEMATICAL SOCIETY of JAPAN. (2) MATSUO published a paper about the general linear regression model. (3) SHIRAHATA submitted a paper with respect to the convergence of multidimensional empirical distribution function. (4) TANIGUCHI submitted a paper about the robustness in time series analysis. (5) FUKUSHIMA and DATE published papers of mathematical foundations of the asymptotic theory.
    Reconsideration : Our study stimulates researches about asymptotic theory of the statistical inference, especially for parametric model of stochastic processes, which is recently developed. These studies should be verified the utility and ability in statistical applications.

  • Long-memory time series; its foundations and applications to economics.

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1988
    -
    1989
     

    OKAMOTO Masanori, ODAKI Mitsuhiro, TANIGUSHI Masanobu, FUJIKOSHI Yasumori, MAEKAWA Kouichi, KIMURA Shigeru

     View Summary

    OKAMOTO generated FGN and fractional ARIMA(O,d,O) and ARIMA(l,d,O)on the computer to simulate long-memory time series. By FGN plus certain sinusoidal components,,he obtained the simulated time series having the same long-memory character as the real exchange rate. He also studied the effects of autoregressive part on fractional ARIMA(l,d,O). He estimate degree d of fractional differencing of ARIMA with additional 1/2 differencing from the relation of periodogram vs frequency. He presented a statistic testing the null hypothesis of Brownian motion vs the alternatives of fractional Brownian motion and commuted its power function. KIMURA & Okamoto studied about models of exchange rate from the point of view of random walk, interest parity, unbiased predictor and time series AR model, in particular about predictability of different models. ODAKI studied the cointegration and common trend under the condition of the existence of constant term. Asymptotic ancillarity in time series was studied by TANIGUCHI. MAEKAWA presented asymptotic expansion of the sample distribution of unknown parameter of spectral density up to the third order. He also reported asymptotic expansion of OLS estimate in nonlinear regression model. FUJIKOSHI made a series of studies on error bounds for asymptotic expansions of the distributions of some multivariate statistics.

  • 確率分布の近似理論と応用に関する研究

    科学研究費助成事業(広島大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1988
     
     
     

     View Summary

    本研究は統計解析の理論展開において重要な役割を演じている確率分布の近似理論の数字的基礎とその統計的推測への応用に関する研究を目的として数理統計学の専門家と関連する数学の専門家によって組織された。研究はセミナーや他大学の関連研究者と研究連絡を行いながら進められた。主要成果は次の通りである。
    成果内容は次の1〜3に分類できる:1.漸近展開の数学的基礎、
    2.漸近的標本分布の導出、
    3.統計的漸近理論。
    1については、尺度混合変数の漸近展開に対して、誤差限界を与えることに成功した。この結果は統計学における種々の分布の漸近展開とその誤差限界の導出に利用できるものである。2については、次の統計量の漸近展開を導出した。(1)ある種の一般化最小二乗推定量、(2)多変量t-分布とそれらの最大、(3)多変量F-分布とそれらの最大、(4)ARMA過程における検定統計量、(5)多変量線型仮説と独立性の検定に対するある種の検定統計量のクラス、(6)多変量成長曲線モデルにおける自己共分散構造に対する尤度比統計量、(7)共分散行列の構造に対する一般検定統計量。3については、(1)多変量線型仮説の検定に関する代表的統計量の比較を、パワーの漸近展開を利用してこれらの統計量を含むクラスで比較し、代表的統計量の特徴をより明確にした。独立性の検定に対しても同様な結果を得た。(2)ARMA過程での検定問題に対して、検定統計量の漸近近似の改良を与えることにより、より精度よく検定することを可能にした。(3)多変量成長曲線モデルで自己共分散構造がある場合の漸近理論の基礎的研究を行った。(4)多変量母集団の選択問題に対して、2段階法に基づく手法を提案し、その漸近的最適性について知見を得た。
    上記は研究目的に直結した主要結果であるが、この他にも各分担者により多くの成果が得られている。

  • 経済時系列における因果性検定の理論的基礎と応用

    科学研究費助成事業(広島大学)  科学研究費助成事業(一般研究(C))

    Project Year :

    1986
     
     
     

     View Summary

    経済時系列における因果性検定の理論的研究として、岡本は一般化されたSimsの非因果性の概念を与え、ベクトルイノベイションの共分散関数が対角ブロックであるという仮定の下で、一般化されたSimsの非因果性と同等な二つの条件を示した。また多変量時系列の場合のノイズ寄与率RPCに相当する統計量MRPCを与えた。これはベクトル成分間の共分散行列と時系列の移動平均過程表現の係数行列とベクトル成分のスペクトルによって表わされる。次いでMRPCに対する漸近的検定統計量を導出した。一方因果性検定の実証的研究として北岡は因果性の検定法およびデータ加工の処理過程にいくつかの相異なる方法が使われている事に注目し、統計的方法の相違及びデータ加工の変化に対して検定結果が頑健かどうかを実証的に検討した。検定法とししては、Granger test,Sims test,Pierce and Haugh testのほかに分散分解法,RPCによるものを取上げ、変数はマネーサプライ、名目GNPのほかにコールレートを加えた3変数の場合について検討を行った。データ処理の前提として、1.Simsフィルター,階差フィルターによる定常化、2.季節ダミー変数,センサスX11法による季節調整済み系列と季節調整なしの原系列、3.変数選択としてコールレートを入れた3変数の場合とこれを除いた2変数の場合について行った。モデル選択はAIC基準によった。主な結論としてはダミー変数による季節調整法とRPCによる検定法が頑健性を有しており、定常化フィルターについてはSimsフィルターは適切ではないことがわかった。前川、谷口、藤越の漸近展開に基づく一連の研究は検定統計量の漸近的性質を導くのに有用と思われる。なお岡本の提案した検定統計量の実証的有用性については何等検討が行われていないので、これは今後に残された課題である。

  • Analysis of Time Series Data: Theory and its Applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1985
    -
    1986
     

    MAEKAWA Koichi, TANIGUCHI Masanobu, FUJIKOSHI Yasunori, KITAOKA Takayoshi, OKAMOTO Masanori B.

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    The results of this projects are associated with the following three area: (1) Asymptotic expansion in time series analysis, (2) Special problems in economic time series, (3) Basic problems in asymptotic expansion. Following the above classification, we describe the main results of our projects.
    (1) Maekawa derived the Edgeworth expansion for the OLS estimator in a ARMAX model and analyzed the resulting formulas. He also obtained the expansion for the four predictors in AR(p) process and compared the finite sample properties of them. Taniguchi developed the theory of the third order asymptotic efficiency of the maximum likelihood estimator in the Gaussian ARMA process and found that a modified MLE in the class D was efficient in that sense.
    (2) Okamoto extended the Sims' noncausality to a more general case and proposed the multivariate relative powe contribution(MRPC) for the causality test in VAR model. Kitaoka compared several test procedures for causality by simulation method under various conditions and found that RPC was the most robust among them.
    (3) Fujikoshi investigated basic problems in the asymptotic expansion. His results seems to be very relevant to the asymptotic expansion in time deries analysis. For example, his method in evaluating the error bound in approximations will be applicable to the time series analysis.

  • Statistical Analysis of Spatial Data

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    1985
    -
    1986
     

    MASE Shigeru, HYAKUTAKE Hiroto, TANIGUTI Masanobu, IWASE Kosei, KUWADA Masanide, SHOUHOUJI Takao

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    Main results of this project are classified as follows:
    1. Theoretical studies of Gibbsian point processes as a basis of the statistical model of spatial data. Especially a general form of size distributions for non-intersecting balls which is important in stereology and a finer approximation formula for partition functions which is important for maximum likelihood estimation of potential functions are obtained.
    2. Image and Graphical analysis of spatial data on computers. Especially an algorithm of drawing speed-dependent Voronoi tasselations was tested and a program package for graphical tools of Fortran was developed.
    3. Combinatorial and Design problems associated with spatial data analysis. Especially a sampling problem of spatial data was discussed.
    4. Analysis of traffic flows. Especially a fitting problem of inverse Gaussian distributions to speed distributions of vehicles was discussed.
    5. The connection and the applicability of methods and concepts of other branches of statistics, e.g. timeseries analysis, asymptotic theory and sequential analysis, were studies.
    6. Applications to practical data. Especially a statistical analysis of individual growth and epidemical studies in a district were undertaken.

  • 大偏差原理と統計学

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    まず大偏差原理の諸結果を整理した。特に統計学に関するものをまとめた。次に従属標本に対しても使える大偏差原理を整理した。これらの結果を時系列モデル,特に時系列回帰モデルに応用した。具体的な結果を以下述べると,回帰関数がグレナンダー条件をみたし,残差がスペクトル密度関数fをもつ正規定常過程で表わせる時系列回帰モデルの尤度比に対する大偏差定理を示した。比率関数は残差のスペクトル,回帰関数のスペクトルで明示的に表わせるが、その詳細な構造は見えにくい。同様の条件下で2次形式及び誤って特定化した尤度比に対しても大偏差定理を示した。次に残差系列が長期記憶構造をもつ時系列回帰モデルの尤度比に関する大偏差定理も与えることができた。この結果は残差が短期記憶構造をもつときと明らかに異なることが判明した。上述の諸結果における比率関数を種々のモデルに対してコンピューターグラフィックスをもちいて図で表わした。視覚的にも種々の新しい知見を得た。最後に、大偏差原理に基づく漸近有効性(バハドール効率)についても、スペクトル-パラメーターの最尤推定量がバハドールの意味で漸近有効であることも見た

  • Research of Statistical Transformation Methodology

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    The purposes of the project are to research some types and methods of parametric and non-parametric transformations of data, to evaluate performances for practical uses, and to develop their extensions. In the project research, we could obtain the following results and some productive findings :We have proposed three extended power-transformations, namely Double-power Normal Transformation (DPNT). Double-power Additive Transformation (DPAT), and Double-power Weighted Transformation (DPWT). Further, we evaluated performances of the proposed transformations by applying to some examples cited in literatures and conducting simulations experiments. These transformations have shown better performances than ordinary power transformation, in normality and homogeneity of observation, and additivity of model.A modified power transformation was proposed to ordinary power transformation. This transformation is completely equal to identity transformation when transformation of data is not necessary. Incidentally, the ordinary power transformation was nearly equal to identity transformation in such case.We have shown inference approach of the power-normal distribution based on grouped observations and their extensive applications. These results was useful in analyses of practical data, especially biomedical and behaviormetric data. Further, the inforence procedure was extended to case which both grouped and ungrouped observations were included.Non-parametric transformation ACE were extended to combine it with SIR and some performances of the approach was evaluated. The computer program of the approach was also developed and produced to the research on many follows.As a control of the power normal distribution, we have investigated log-gamma distribution and evaluated some its performances relative to the power normal distribution of fitting to some practical data, and further have shown extensive applications to medical field.We have investigated possibility of transforming qualitative data to their quantitative forms by using the power transformation. Particularly, we evaluated the appropriateness of log-transformation to data which had Poisson distribution

  • Research of Information-geometric Properties in Statistical Estimation Theory

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    We studied information-geometric properties in the statistical estimation theory under the following three themes(1) The information loss of the maximum likelihood estimator and its information-geometric aspects (by N.INAGAKI and E.KUMAGAI) The asymptotic representaion of the information loss of the maximum likelihood estimator is shown by B.Efron and S.Amari due to the statistical curvature and Fisher information. We obtained an algorism to calculate the center and radius with the statistical curvature which we call the circular mechanism of the likelihood function. We discussed the multidimensional sphere model as the extensions of Fisher' s circle and sphere models for 2 and 3 dimen sions, respectively. We obtained the exact infromation loss of the maximum likelihood estimator of the angle parameter in the k-dimensional sphere model and showed its asymptotic behavior which converges to the Efron-Amari' s asymptotic re-presentation. We studied the duality of parameter and observation in the exponential type of distributions by the Legendre convex duality of the cumulant generating function, which leads to the asymptotic properties of maximum likelihood estimator.(2) Estimation problems in spacial data and time series analysis (T.ISOGAI and M.TANIGUCHI) : The regression problems of spacial data were studied due to parametric and empirical variograms. We had many results for time series analysis, prediction theory and their applications.(3) Estimation problems in generalized linear models (S.SHIRAHATA and S.AKI) Topics of dose response analysis, life time analysis, and so on, and applications of gene-ralized linear models were studied

  • セミパラメトリック手法に対する高次漸近理論

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    多次元非正規定常過程のスペクトル密度行列の汎関数に基づいて種々の重要な時系列指標のセミパラメトリックな推定、検定等の漸近理論を構築した。この場合、汎関数に現れるスペクトル密度行列を推定するときは、ノンパラメトリックなスペクトル推定量を用いた。この基礎理論に基づいて、経済指標のセミパラメトリック推定、検定、をおこなった。また時系列の判別分析において、セミパラメトリックな判別統計量を提案し、漸近的性質をしらべた。従来のカルバック、レイブラーの情報量に基づく判別統計量との比較も行った。また提案された判別統計量は、地震波の判別に応用された。即ち、通常の地震波と鉱山の爆発による地震波の判別に、応用され、判別結果が大変良好であることが判明した。また高次の漸近論では一般的な検定統計量のクラスを定義し、これにたいして、高次の検出力を一般的な形で評価した。以上は定常時系列に関する議論であるが、局所定常時系列にたいして漸近理論の基礎を構築し、これに基づいて、時系列の定常性の検定の基礎的議論をおこなった。その他、長期記憶課程を撹乱項にもつ時系列回帰モデルに対する局所漸近正規性の証明もおこなった

  • Statistical Inference for Discrete Patterns

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    We have studied waiting time distributions of runs and patterns in random structures such as sequences of random variables and random directed trees. The following results are derived.1. We have obtained the exact distribution of the number of "1" -runs of a specified length on {0, 1} -valued Markov trees. This result can be applied to calculate the reliability of a consecutive system on a directed tree. We also obtained the exact distribution of the life time of the consecutive system on the directed tree.2. We have studied exact distributions of sooner and later waiting times for runs in Markov dependent bivariate trials. We have given systems of linear equations with respect to conditional probability generating functions of the waiting times and have solved them. This result can be applied to calculate the reliability of the linear connected- (r, s) -out-of- (r+1, n) : F lattice system.3. We have introduced a Markov chain imbeddable vector of multinomial type and a Markov chain imbeddable variables of returnable type and have discussed some of their properties. By using the result we have derived the distribution of numbers of occurrences of runs of specified lengths in a sequence of multi-state trials.4. We have introduced a unified counting scheme for runs called 1-overlapping counting. We have given exact probability generating function of the number of 1-overlapping 1-runs of a specified length in some dependent random sequences such as a Markov chain and a heigher order Markov chain.5. We have introduced a new type of dependent sequence called a binary sequence of order (k, r) and have derived the exact distributions of sooner and later waiting times for success and failure runs in the sequence

  • integrated research with the theory applications of statistics

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    For two years from October 2000 to January 2002, we had various symposiums throughout Japan concerned with Multivariate analysis, Asymptotic distribution, Factor Analysis, Non-linear statistical modeling, Covariance structural analysis, Environmental statistics, Data-mining, Measurement economy and Measurement finance, Multivariate graphical method, Quality of Life, from theoretical to applied Statistics. In each symposium we discussed the reliability of theoretical results and their applications to various statistical problems. Also, we invited foreign statisticians who are eminent in each research field. Through their symposium we constructed the feedback system between theoretical and applied statisticians. Finally we made the reports of research papers consisting of 1224 pages.We achieved the purpose of this research project with many valuable results

  • 時系列セミパラメトリックモデルに対する高次漸近理論

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    定常過程のスペクトル密度関数の推定において、このノンパラメトリックな推定量と適合された母数型スペクトル密度関数の距離を最小にする母数推定量を最小コントラスト推定量ということにする。この推定量は十分ひろいクラスの距離に対して1次漸近有効となる。したがって、この推定量の高次の漸近挙動に興味がある。通常の母数推定論において、1次漸近有効な推定量はバイアスを調整すれば、自動的に2次漸近有効になる。ところが、最初にのべたセミパラメトリックな推定において、1次漸近有効な最小コントラスト推定量はバイアス調整しても一般に2次漸近有効にならないということを示すことができた。これは、セミパラメトリックな推定論とパラメトリックな推定論との興味ある差異を示している。近年、金融時系列解析に熱い視線がそそがれてきている。この分野ではARCHモデルが頻繁にもちいられている。金融時系列の実証分析よりARCHモデルの残差系列の分布は裾が長い傾向があることが知られている。そこで、まずARCHモデルのボラテリテェーの未知母数を条件つき最小2乗法で推定し、これより推定された残差系列をつくる。この残差系列に母数型の確率密度関数をalpha-divergenceを用いて適合しノンパラメトリックな確率密度関数との距離を最小にするように母数を推定する。これで得られた推定量について漸近分布を求めた。ここで、注意すべきは、この漸近分布はARCHモデルのボラテリテェーの母数の推定量の漸近分布に依存しており、通常のARMAモデル等の残差と著しく異なっていることを示した。以上の推定法はARCHモデルの残差分布上の汎関数を定義するものだが、真の残差分布がずれた場合の、この汎関数のロバスとネスについてもしらべ、どのような分布族に対してロバストかを見た

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Misc

 

Overseas Activities

  • 金融時系列解析の研究

    2012.04
    -
    2013.03

    イタリア  

    フランス  

    ベルギー  

Internal Special Research Projects

  • 高次交差数に基づく最適統計推測理論の構築とその応用

    2017   青嶋 誠

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    我々の身の回りに起こる自然現象、社会現象からのデータは、ほとんどが、上昇、下降の動きを表す列で記述される。数学的には現象を記述する確率過程を&nbsp; がレベル 0 と交差する点の数を D&nbsp; とする。 微分過程(離散時間の場合は差分過程)のレベル 0 との交差数をを並べた ベクトルを高次交差( Higher Order Crossings (HOC))と呼ぶ。関与の確率過程が定常でスペクトル分布関数 F を持つとき HOC の期待値は F の積分汎関数で表される。HOC 解析の分野では種々の基礎解析がなされているが、統計的最適推測論の構築は極めて未開な状態である。以上を基礎認識として本研究ではスペクトル密度関数がシャープなピークで乱されているとき、HOC の頑健性を通常の Whittle 推定量のそれと比較して前者がある種の頑健性を持つことを示した。

  • 高次元時系列データの数理理論構築とその諸分野への応用

    2013  

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    本研究では、高次元データへの統計手法の開発と応用、安定過程に対する統計推測、時系列に対する滑らかでないコントラスト関数による推測理論の構築、従属データに対する経験尤度法の使用、また一般化モーメント法の開発を行った。特に、安定過程に対しては、自己正規化変換をしたピリオドグラムに基づく経験尤度法の提案と経験尤度比や経験尤度推定量の漸近分布の導出を行い、この分野に新しい風を入れた。多次元非正規収益率過程へのポートフォリオ係数の推測についても、高次モーメントに基づく推定量の動きを明らかにした。また極めて一般的な確率過程に対する適合度検定として、一般化ポートマントウ型検定を提案して、これが漸近的にカイ2乗分布に従うための条件を明らかにした。因果性検定では、Whittle 尤度に基づいて同時因果性を検定する統計量の提案し、その漸近分布を明らかにした。近接単位根過程に対しても、検定統計量の漸近特性を極めて一般的な設定で展開した。時系列の補間は、欠測値を含むデータに有効であるが、時系列の線形補間誤差に基づくコントラスト関数による推測論も展開した。意外な結果としては、このコントラストによる推定量は、一般に漸近有効にならないことを示した。通常の有効推定量は、線形予測誤差を最小にする推定量として特徴づけられるが、過去と未来の情報を使う補間誤差最小基準でこのような結果が得られることが判明した。 課題に関係するシンポジュームも、下記のように開催し活発な議論が行われた。(1)「高次元データに関連する統計理論の新展開とその応用」、 於 小樽商科大学、開催責任者:劉慶豊2013年9月5日ー7日。(2)「一般化線形モデルの最新の展開とその周辺」、於 千葉大学、開催責任者:汪金芳 2013年11月8日ー10日。(3)「統計科学の新展開」、於 金沢大学、開催責任者:星野伸明 2013年11初27日ー29日。(4)「Stable Process, Semimartingale, Finance & Pension Mathematics」於 早稲田大学、開催責任者:谷口正信、 Dou, X. and 濱田健太。 上記シンポジューム報告は下記:http://www.taniguchi.sci.waseda.ac.jp/kakenhoukoku2011.html においた

  • 時系列解析における縮小推定量の研究

    2013  

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    独立標本での縮小推定量の研究には歴史があり、多様な研究がなされてきた。従属標本の統計解析である時系列解析では、縮小推定量の研究は端緒についたばかりと言える。本研究では、p 次の自己回帰モデルの自己回帰係数の推定に於いて縮小推定量を提案した。従来は、最小2乗推定量や疑似最尤推定量で推測されてきた。本研究の前半では、提案した縮小推定量と従来の最小2乗推定量の平均2乗誤差(MSE)を比較して、MSE の意味で縮小推定量が最小2乗推定量を改善する条件を求めた。 また縮小係数に未知量が入るので、これを推測した推定量のよさも調べた。数値的には、自己回帰過程が単位根過程から離れるにつれて縮小推定量が最小2乗推定量を、よりよく改善することを見た。本研究の後半では、定常時系列の予測に縮小型予測子を導入した。定常過程の最適線形予測子は、そのスペクトル密度関数が既知であれば、完全に特定される。実際にはスペクトル密度関数は観測系列から推測されるので、誤特定化が常に起こっている。誤特定されたスペクトル密度関数から形式的に求めた最適予測子( misspecified best predictor) の予測誤差は、すでに評価されている。本研究では、この状況で、misspecified best predictor の縮小予測子を提案した。この縮小予測子の予測誤差を評価して、これが missecified best predictor のそれを改善する条件をもとめた。また、この縮小予測子は縮小係数に期待値を含むので、これの標本バージョンを構成し、この縮小予測子のよさを議論した。自己回帰モデルで縮小予測子の動きを数値的にみても、従来型の予測子を改善していることを見た。従属標本に対する縮小推定、縮小予測子の研究は、端緒についたばかりであるが、従来の推定量、予測子を改善しており、更なる展開が必要となろう。近年、金融時系列解析が理論、応用ともに発展してきており、縮小推定論を、非線形時系列モデル、非定常時系列モデルの未知指標の推測に展開する必要があろう。この課題も、上記の基礎結果が、よい指針を与えよう。

  • 時系列解析と統計的金融工学の総合的研究

    2005  

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    時系列解析において非線形、非定常、非正規確率過程に対する局所漸近正規性の証明を行いこれに基づく最適推測、検定、判別の基礎理論を構築した。また時系列解析における経験尤度法、局所 Whittle 尤度に基づく推測論等の基礎理論も発展させた。局所 Whittle 尤度に基づく、スペクトル推定量は、簡単な母数型スペクトルを適合して、その母数を周波数に依存させる形で推定量を得た。これは、従来の非母数的なスペクトル推定量を最小2乗誤差の意味で改善する等のよさをもつことが、数値的にも示された。経験尤度法では従来のスペクトル型が明示的にわかっているという状況でなくても、種々の時系列指標の信頼区間を与えることが可能になり、これも従来の時系列解析に新しい手法を提案することができた。応用面では、最適ポートフォリオ係数の漸近有効な推定量で推測することを試み、従来とは異なったより一般的な仮定;収益率過程は(1)非正規定常過程、(2)非正規局所定常過程に対して、従来の推定量の漸近有効性と、(1)と(2)の仮定のもとでポートフォリオ係数の漸近有効な推定量を提案した。これは時系列解析の理論結果の金融工学への応用である。また、時系列の判別手法を非正規、非定常過程に応用し、時間依存するスペクトル密度関数の擬距離を用いて種々の企業の株価データをクラスター解析し、金融工学における格付けが、このような時系列構造をもつデータに関しても可能であることがわかった。従来の格付けは独立標本の判別解析に基づいており、このような手法は新しいアプローチとなる。

  • 時系列解析における縮小統計量の研究

    2004  

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    独立標本に対しては、縮小統計量の研究は極めて詳細かつsyatematic に進められてきた。しかしながら時系列のような従属な標本に対してはこの様な研究は皆無といってよい。そこで本研究課題では、種々の時系列モデルでの縮小推定量の基礎理論を構築することをもくろんだ。具体的には、多次元正規過程の平均ベクトルの James-Stein 型推定量の平均2乗誤差をスペクトル密度行列の言葉で評価し、通常の標本平均を平均2乗誤差の意味で改善する十分条件を明らかにした。また関与の確率過程が長期記憶過程であるときもJames-Stein型推定量が標本平均を平均2乗誤差の意味で改善するための十分条件を求めた。これは、長期記憶パラメーターと短期記憶部のスペクトルの言葉で表現でき、改善のようすを種々の時系列モデルで数値的にも見た。 さらに時系列回帰モデルで回帰関数がグレナンダー条件を満たし、残差系列が正規定常過程を考える。このとき、回帰係数のJames-Stein型推定量と通常の最小2乗推定量の平均2乗誤差を回帰スペクトルと残差スペクトルの言葉で表し、James-Stein型推定量が最小2乗推定量を平均2乗誤差に意味で改善するための十分条件を求めた。種々の回帰スペクトルと残差スペクトルに対して、この改善のようすを数値的に検証した。 時系列の縮小推定量の研究は端緒についたばかりで、今後、分散量に対する縮小推定量の研究や、局所定常過程に関する縮小推定量の振る舞いの研究をすすめる予定である。

  • 時系列解析における理論と応用の総合的研究

    2004  

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    本研究課題では次の4点を遂行した。(1)非定常時系列解析:非定常時系列の重要なクラスである非正規局所定常過程の推測に関して、まず局所漸近正規性(LAN)を示し   これに基づいて、漸近最適推測、検定、判別を記述した。さらには撹乱項の分布が未知である場合、これを非母数的に推測し、   これに基づいて、ダイナミクス部の漸近最適推定も論じた。(2)時系列回帰モデルのセミパラメトリック推定の高次漸近理論の構築:残差項が定常過程で回帰部分がある種のグレナンダー   条件を満たす場合のHannan型の回帰係数推定量の2次の漸近分布を求め、2次有効性の議論を行った。(3)非線形時系列の推定論:非線形時系列の極めて一般的なモデル族であるCHARNモデルに対して、LAN定理を示し、これに基づく   漸近最適推定論と検定論を構築した。(4)上記(1)-(3)の結果の実際問題への応用:(1)の結果の応用としては、局所定常過程の判別理論を種々の金融時系列の   クラスター解析に応用し、非定常時系列データに基づく企業の格付けへの可能性を示した。また(2)の高次漸近理論の応用と   して、収益率を非正規従属過程とした場合のオプションの価格評価を漸近展開をもちいて行った。(3)の応用としては、ある   疾病患者の脳波と筋電波のCHARNモデルを適合し、生体工学的に重要な脳波と筋電波の関係を把握した。

  • 局所定常過程の統計解析

    2003  

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    (I)局所定常過程の統計解析の基礎研究を行った。具体的な成果としては(I-1)非正規局所定常過程に対する局所漸近正規性(Local Asymptotic Normality (LAN))を示した。(I-2)LAN に基づき、局所定常過程の未知母数推定、検定、判別の基礎理論を構築した。   これは、最尤推定量の漸近最適性、Central Sequence に基づいた検定の漸近最適性。   擬似尤度に基づいた判別統計量の漸近最適性等である。(II)非正則な時系列モデルの推測の基礎理論を構築した。具体的には(II-1)連続でないスペクトル密度関数の推測論。このような時系列モデルはLAN性をもたず、上述の   結論が成立たないことをしめした。(II-2)この場合は最尤推定量は漸近最適とならずBayes推定量が漸近最適となることが判明した。(III) 生体工学データへの時系列解析の応用。これは、ある疾病の患者の脳波と筋電波の相関関連解析に 極めて一般的な多次元金融時系列モデルを適用し、意味ある結果を得た。(III-1)まず、このモデル(CHARN)に対してLAN性を示した。(III-2)これに基づき、漸近最適な推測、検定論を行った。(III-3)脳波、筋電波に適用し、今までにない、これらの相関構造をあきらかにした。

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