Updated on 2022/05/21

写真a

 
NISHIYAMA, Yoichi
 
Affiliation
Faculty of International Research and Education, School of International Liberal Studies
Job title
Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

  • Faculty of International Research and Education   Graduate School of International Culture and Communication Studies

Education

  • 1993.04
    -
    1994.03

    Osaka University  

  • 1991.04
    -
    1993.03

    Osaka University  

  • 1987.04
    -
    1991.03

    Osaka University   School of Science   Department of Mathematics  

Degree

  • 1993.03   Osaka University   (Master of Engineering)

  • 1998.05   Utrecht University   (Ph. D.)

Research Experience

  • 2016.04
    -
    Now

    Faculty of International Research and Education, Waseda University   Professor

  • 2015.04
    -
    2016.03

    Faculty of International Research and Education, Waseda University   Associate Professor

  • 2008.04
    -
    2015.03

    The Institute of Statistical Mathematics   Associate Professor

  • 1994.04
    -
    2008.03

    The Institute of Statistical Mathematics   Assistant Professor

Professional Memberships

  •  
     
     

    日本数学会

  •  
     
     

    日本統計学会

 

Research Areas

  • Statistical science

  • Applied mathematics and statistics

  • Basic mathematics

Research Interests

  • Mathematical Statistics

  • Probability Theory

  • Data Science

  • Martingales

  • Random Fields

Papers

  • Weak convergence of marked empirical processes in a Hilbert space and its applications

    Koji Tsukuda, Yoichi Nishiyama

    ELECTRONIC JOURNAL OF STATISTICS   14 ( 2 ) 3914 - 3938  2020.10  [Refereed]

  • Moment convergence of $Z$-estimators

    Ilia Negri, Yoichi Nishiyama

    STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES   20 ( 3 ) 387 - 397  2017.10  [Refereed]

     View Summary

    The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.

    DOI

  • The Dantzig selector for diffusion processes with covariates

    Kou Fujimori, Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   47 ( 1 ) 59 - 73  2017.06  [Refereed]

    DOI

  • $Z$-process method for change point problems with applications to discretely observed diffusion processes

    Ilia Negri, Yoichi Nishiyama

    STATISTICAL METHODS AND APPLICATIONS   26 ( 2 ) 231 - 250  2017.06  [Refereed]

     View Summary

    The aim of this paper is to develop a general, unified approach, based on some partial estimation functions which we call "Z-process", to some change point problems in mathematical statistics. The method proposed can be applied not only to ergodic models but also to some models where the Fisher information matrix is random. Applications to some concrete models, including a parametric model for volatilities of diffusion processes are presented. Simulations for randomly time-transformed Brownian bridge process appearing as the limit of the proposed test statistics are performed with computer intensive use.

    DOI

  • The $l_q$ consistency of the Dantzig selector for Cox's proportional hazards model

    Kou Fujimori, Yoichi Nishiyama

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   181   62 - 70  2017.02  [Refereed]

     View Summary

    The Dantzig selector for the proportional hazards model proposed by D.R. Cox is studied in a high-dimensional and sparse setting. We prove the lq consistency for all q is an element of [1, infinity] of some estimators based on the compatibility factor, the weak cone invertibility factor, and the restricted eigenvalue for certain deterministic matrix which approximates the Hessian matrix of log partial likelihood. Our matrix conditions for these factors are weaker than those of previous researches. (C) 2016 Elsevier B.V. All rights

    DOI

  • On $L_2$ space approach to change point problems

    Koji Tsukuda, Yoichi Nishiyama

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   149   46 - 59  2014.06  [Refereed]

     View Summary

    This paper deals with some change point problems based on the general theory of weak convergence in Hilbert spaces. In particular, we develop an L-2 space approach to handle Anderson-Darling type statistics, which was taken for goodness of fit test problems, to change point problems for which more delicate arguments are necessary. (C) 2014 Elsevier B.V. All rights reserved.

    DOI

  • Asymptotically distribution free test for parameter change in a diffusion process model

    Ilia Negri, Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   64 ( 5 ) 911 - 918  2012.10  [Refereed]

     View Summary

    A test procedure to detect a change in the value of the parameter in the drift of a diffusion process is proposed. The test statistic is asymptotically distribution free under the null hypothesis that the true parameter does not change. Also, the test is shown to be consistent under the alternative that there exists a change point.

    DOI

  • Some problems in nonparametric inference for the stress release process related to the local time

    Takayuki Fujii, Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   64 ( 5 ) 991 - 1007  2012.10  [Refereed]

     View Summary

    This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role.

    DOI

  • ノンパラメトリック変化点問題に対する順位統計量について

    西山 陽一

    統計数理   60   215 - 218  2012.06  [Refereed]

  • A rank statistic for non-parametric $k$-sample and change point problems

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   41   67 - 73  2011.09  [Refereed]

    DOI

  • Goodness of fit test for small diffusions by discrete time observations

    Ilia Negri, Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   63 ( 2 ) 211 - 225  2011.04  [Refereed]

     View Summary

    We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete time observation of the processes, and the diffusion coefficient is a nuisance function which is "estimated" in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternative.

    DOI

  • Estimation for the invariant law of an ergodic diffusion process based on high-frequency data

    Yoichi Nishiyama

    JOURNAL OF NONPARAMETRIC STATISTICS   23 ( 4 ) 909 - 915  2011  [Refereed]

     View Summary

    Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t(0)(n) < t(1)(n) < ... < t(n)(n) such that t(n)(n) -> infinity and n Delta(1+ p)(n) -> 0, where Delta(n) = max(1 <= i <= n) |t(i)(n) - t(i-1)(n)|, with p is an element of (0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

    DOI

  • Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach

    Hiroki Masuda, Ilia Negri, Yoichi Nishiyama

    JOURNAL OF NONPARAMETRIC STATISTICS   23 ( 2 ) 237 - 254  2011  [Refereed]

     View Summary

    We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternatives.

    DOI

  • Impossibility of weak convergence of kernel density estimators to a non-degenerate law in $L_2(\mathbb{R}^d)$

    Yoichi Nishiyama

    JOURNAL OF NONPARAMETRIC STATISTICS   23 ( 1 ) 129 - 135  2011  [Refereed]

     View Summary

    It is well known that the kernel estimator [image omitted] for the probability density f on d has pointwise asymptotic normality and that its weak convergence in a function space, especially with the uniform topology, is a difficult problem. One may conjecture that the weak convergence in L2(d) could be possible. In this paper, we deny this conjecture. That is, letting [image omitted], we prove that for any sequence {rn} of positive constants such that rn=o(root n), if the rescaled residual rn(f<SU</SUn-fn) converges weakly to a Borel limit in L2(d), then the limit is necessarily degenerate.

    DOI

  • On $Z$-estimation by rounded data

    Yoichi Nishiyama

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   141 ( 1 ) 287 - 292  2011.01  [Refereed]

     View Summary

    It is often assumed in statistics that the random variables under consideration come from a continuous distribution. However, real data is always given in a rounded (discretized) form. The rounding errors become serious when the sample size is large. In this paper, we consider the situation where the mesh of discretization tends to zero as the sample size tends to infinity, and give some sets of sufficient conditions under which the rounding errors can be asymptotically ignored, in the context of Z-estimation. It is theoretically proved that the mid-point discretization is preferable. (C) 2010 Elsevier B.V. All rights reserved.

    DOI

  • Moment convergence of $M$-estimators

    Yoichi Nishiyama

    STATISTICA NEERLANDICA   64 ( 4 ) 505 - 507  2010.11  [Refereed]

     View Summary

    This study extends the rate of convergence theorem of M-estimators presented by van der Vaart and Wellner (weak convergence and empirical processes: with applications to statistics, Springer-Verlag, Newyork, 1996) who gave a result of the form r(n)((theta) over cap (n)-theta(0)) = O(P)(1) to a result of the form sup(n)E vertical bar r(n)((theta) over cap (n) - theta(0)) vertical bar (p) < infinity, for any p >= 1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.

    DOI

  • Nonparametric inference in multiplicative intensity model by discrete time observation

    Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   62 ( 5 ) 823 - 833  2010.10  [Refereed]

     View Summary

    This paper deals with nonparametric inference problems in the multiplicative intensity model for counting processes. We propose a Nelson-Aalen type estimator based on discrete observation. The functional asymptotic normality of the estimator is proved. The limit process is the same as that in the continuous observation case, thus the proposed estimator based on discrete observation has the same properties as the Nelson-Aalen estimator based on continuous observation. For example, the asymptotic efficiency of proposed estimator is valid based on less information than the continuous observation case. A Kaplan-Meier type estimator is also discussed. Nonparametric goodness of fit test is considered, and an asymptotically distribution free test is proposed.

    DOI

  • Goodness of fit test for ergodic diffusions by tick time sample scheme

    Ilia Negri, Yoichi Nishiyama

    STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES   13 ( 1 ) 81 - 95  2010.04  [Refereed]

     View Summary

    We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct a test based on the data observed discretely in space, that is, the so-called tick time sampled data. It is proved that the asymptotic distribution of our test under the null hypothesis is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. It is also shown that the test is consistent under any fixed alternative. © Springer Science+Business Media B.V. 2010.

    DOI

  • Review on goodness of fit tests for ergodic diffusion processes by different sampling schemes

    Ilia Negri, Yoichi Nishiyama

    ECONOMIC NOTES   39 ( 1-2 ) 91 - 106  2010.02  [Refereed]

     View Summary

    We review some recent results on goodness of fit test for the drift coefficient of a one-dimensional ergodic diffusion, where the diffusion coefficient is a nuisance function which however is estimated. Using a theory for the continuous observation case, we first present a test based on deterministic discrete time observations of the process. Then we also propose a test based on the data observed discretely in space, that is, the so-called tick time sample scheme. In both sampling schemes the limit distribution of the test is the supremum of the standard Brownian motion, thus the test is asymptotically distribution free. The tests are also consistent under any fixed alternatives. © 2010 The Authors Economic Notes © 2010 Banca Monte dei Paschi di Siena SpA.

    DOI

  • Uniform rate of convergence of smoothed Nelson-Aalen estimator

    Nishiyama, Yoichi (The, Institute of, Statistical Mathematics

    Proceedings of the Institue of Statistical Mathematics   58   131 - 135  2010  [Refereed]

  • 射影推定量についての一注意

    西山 陽一

    統計数理   58   127 - 130  2010  [Refereed]

  • A sufficient condition for observation noise not to affect the extreme value distribution

    Yoichi Nishiyama, Takaaki Shimura

    Proceedings of the Institute of Statistical Mathematics   57   443 - 447  2009.12  [Refereed]

  • Two sample problem for rounded data

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   39   233 - 238  2009.12  [Refereed]

    DOI

  • Asymptotic theory of semiparametric $Z$-estimators for stochastic processes with applications to ergodic diffusions and time series

    Yoichi Nishiyama

    THE ANNALS OF STATISTICS   37 ( 6A ) 3555 - 3579  2009.12  [Refereed]

     View Summary

    This paper generalizes a part of the theory of Z-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation theta (sic) Psi(n) (theta, (h) over cap (n)) = 0 with an abstract nuisance parameter h when the compensator of Psi(n) is random. As its application, we consider the estimation problem in an ergodic diffusion process model where the drift coefficient contains an unknown, finite-dimensional parameter theta and the diffusion coefficient is indexed by a nuisance parameter h from an infinite-dimensional space. An example for the nuisance parameter space is a class of smooth functions. We establish the asymptotic normality and efficiency of a Z-estimator for the drift coefficient. As another application, we present a similar result also in an ergodic time series model.

    DOI

  • Goodness of fit test for ergodic diffusion processes

    Ilia Negri, Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   61 ( 4 ) 919 - 928  2009.12  [Refereed]

     View Summary

    A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.

    DOI

  • Goodness-of-fit test for a nonlinear time series

    Yoichi Nishiyama

    JOURNAL OF TIME SERIES ANALYSIS   30 ( 6 ) 674 - 681  2009.11  [Refereed]

     View Summary

    Goodness-of-fit test in a general model of nonlinear time series is considered. We present an asymptotically distribution-free test based on a random field of innovation martingales. Its consistency under any fixed alternative is also proved.

    DOI

  • Nonparametric goodness of fit tests for diffusion processes

    Nishiyama, Yoichi (The, Institute of, Statistical Mathematics

    Proceedings of the Institute of Statistical Mathematics   57   83 - 95  2009.06  [Refereed]

  • Donsker's theorem for discretized data

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   38   505 - 515  2008.12  [Refereed]

    DOI

  • Nonparametric estimation and testing time-homogeneity for processes with independent increments

    Yoichi Nishiyama

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   118 ( 6 ) 1043 - 1055  2008.06  [Refereed]

     View Summary

    We consider a nonparametric estimation problem for the Levy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an l(infinity)-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the Levy measure. Our result is a fruit of the empirical process theory and the martingale theory. (C) 2007 Elsevier B.V. All rights reserved.

    DOI

  • On the paper "Weak convergence of some classes of martingales with jumps"

    Yoichi Nishiyama

    THE ANNALS OF PROBABILITY   35 ( 3 ) 1194 - 1200  2007.05  [Refereed]

     View Summary

    This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685-712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniques developed in the modem theory of empirical processes.

    DOI

  • Test for parameter change in diffusion processes by cusum statistics based on one-step estimators

    Sangyeol Lee, Yoichi Nishiyama, Nakahiro Yoshida

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   58 ( 2 ) 211 - 222  2006.06  [Refereed]

    Authorship:Corresponding author

     View Summary

    In this paper, we consider the problem of testing for a parameter change using the cusum test based on one-step estimators in diffusion processes. It is shown that under regularity conditions the cusum test statistic has the limiting distribution of a functional of Brownian bridge.

    DOI

  • Weak convergence of some classes of martingales with jumps

    Yoichi Nishiyama

    THE ANNALS OF PROBABILITY   28 ( 2 ) 685 - 712  2000.04  [Refereed]

     View Summary

    This paper deals with weak convergence of stochastic integrals with respect to multivariate point processes. The results are given in terms of an entropy condition for partitioning of the index set of the integrands, which is a sort of L-2-bracketing. We also consider l(infinity)-valued martingale difference arrays, and present natural generalizations of Jain-Marcus's and Ossiander's central limit theorems. As an application, the asymptotic behavior of log-likelihood ratio random fields in general statistical experiments with abstract parameters is derived.

  • A maximal inequality for continuous martingales and $M$-estimation in a Gaussian white noise model

    Yoichi Nishiyama

    THE ANNALS OF STATISTICS   27 ( 2 ) 675 - 696  1999.04  [Refereed]

     View Summary

    Some sufficient conditions to establish the rate of convergence of certain M-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and nonparametric maximum Likelihood estimation, for the regression function. The results are shown by means of a maximal inequality for continuous martingales and some techniques developed recently in the context of empirical processes.

  • Some central limit theorems for $\ell^\infty$-valued semimartingales and their applications

    Yoichi Nishiyama

    PROBABILITY THEORY AND RELATED FIELDS   108 ( 4 ) 459 - 494  1997.08  [Refereed]

     View Summary

    This paper is devoted to the generalization of central limit theorems for empirical processes to several types of l(infinity)(Psi)-valued continuous-time stochastic processes t squiggly right arrow X-t(n) = (X-t(n, psi) is an element of Psi), where Psi is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t squiggly right arrow X-t(n, psi) is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented. We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior of log-likelihood ratio random fields of certain continuous semimartingales is derived.

  • Local asymptotic normality of a sequential model for marked point processes and its applications

    Yoichi Nishiyama

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   47 ( 2 ) 195 - 209  1995.06  [Refereed]

     View Summary

    This paper deals with statistical inference problems for a special type of marked point processes based on the realization in random time intervals [0, tau(u)]. Sufficient conditions to establish the local asymptotic normality (LAN) of the model are presented, and then, certain class of stopping times tau(u) satisfying them is proposed. Using these stopping rules, one can treat the processes within the framework of LAN, which yields asymptotic optimalities of various inference procedures. Applications for compound Poisson processes and continuous time Markov branching processes (CMBP) are discussed. Especially, asymptotically uniformly most powerful tests for criticality of CMBP can be obtained. Such tests do not exist in the case of the non-sequential approach. Also, asymptotic normality of the sequential maximum likelihood estimators (MLE) of the Malthusian parameter of CMBP can be derived, although the non-sequential MLE is not asymptotically normal in the supercritical case.

▼display all

Books and Other Publications

  • Martingale Methods in Statistics

    Yoichi Nishiyama

    CRC Press, Taylor & Francis Group  2022 ISBN: 9781466582811

  • Statistical Analysis by the Theory of Martingales (In Japanese)

    Yoichi Nishiyama

    Kindaikagakusha  2011.10

  • Entropy Methods for Martingales

    Yoichi Nishiyama

    CWI Tracts  2000

Misc

Awards

  • JSS Ogawa Prize

    2009.09  

Research Projects

  • 高次元マルチンゲール理論とその統計的応用

    科研費基盤研究(C)

    Project Year :

    2018.04
    -
    2023.03
     

    西山 陽一

  • 超高次元の確率解析手法による統計的推測

    科研費基盤研究(C)

    Project Year :

    2015.04
    -
    2018.03
     

    西山 陽一

  • 無限次元の弱収束理論と統計的応用

    科研費基盤研究(C)

    Project Year :

    2012.04
    -
    2015.03
     

    西山 陽一

  • メトリック・エントロピー法の統計的応用

    科研費基盤研究(C)

    Project Year :

    2009.04
    -
    2012.03
     

    西山 陽一

Presentations

  • A stochastic maximal inequality, weak convergence of infinite-dimensional martingales, and semiparametric statistics

    西山 陽一  [Invited]

    日本数学会 2013 年度秋季総合分科会 

    Presentation date: 2013.09

  • Adaptive semiparametric estimation for diffusion processes

    Yoichi Nishiyama  [Invited]

    The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting 

    Presentation date: 2012.07

  • Bracketing CLT for martingales

    Yoichi Nishiyama  [Invited]

    52th ISI World Statistical Congress 

    Presentation date: 1999.08

  • マルチンゲール確率場に対するエントロピー法とその統計的推測への応用

    西山 陽一  [Invited]

    日本数学会 1999 年度年会 

    Presentation date: 1999.03

 

Syllabus

▼display all

Teaching Experience

  • Graph Theory

    Waseda University  

  • Linear Algebra and Its Applications

    Waseda University  

  • Social Studies and Communication

    Waseda University  

  • First Year Seminar A

    Waseda University  

  • Software and Data Science

    Waseda University  

  • Discrete Mathematics

    Waseda University  

  • Linear Algebra

    Waseda University  

  • 確率論

    早稲田大学  

  • 確率と確率過程 A

    早稲田大学  

  • ノン・セミパラメトリック統計推測

    総合研究大学院大学  

  • 確率過程の統計解析

    総合研究大学院大学  

  • 推測数理概論

    総合研究大学院大学  

▼display all

 

Committee Memberships

  • 2013
    -
    2015

    日本統計学会  会誌編集理事(欧文)

  • 2010
    -
    2012

    The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting 2012  Local organizing comittee

  • 2009
    -
    2010

    日本数学会  評議員

  • 2007
    -
    2009

    日本数学会  和文誌「数学」編集委員

  • 2007
    -
    2008

    統計学関連連合大会  企画委員