2022/10/01 更新

写真a

ニシヤマ ヨウイチ
西山 陽一
所属
国際学術院 国際教養学部
職名
教授

兼担

  • 理工学術院   大学院基幹理工学研究科

  • 国際学術院   国際コミュニケーション研究科

学歴

  • 1993年04月
    -
    1994年03月

    大阪大学   基礎工学研究科   数理系専攻 博士後期課程(中退)  

  • 1991年04月
    -
    1993年03月

    大阪大学   基礎工学研究科   数理系専攻 博士前期課程  

  • 1987年04月
    -
    1991年03月

    大阪大学   理学部   数学科  

学位

  • 1993年03月   大阪大学   修士(工学)

  • 1998年05月   ユトレヒト大学   学術博士

経歴

  • 2016年04月
    -
    継続中

    早稲田大学 国際学術院   教授

  • 2015年04月
    -
    2016年03月

    早稲田大学 国際学術院   准教授

  • 2008年04月
    -
    2015年03月

    統計数理研究所   准教授

  • 1994年04月
    -
    2008年03月

    統計数理研究所   助手・助教

所属学協会

  •  
     
     

    日本数学会

  •  
     
     

    日本統計学会

 

研究分野

  • 統計科学

  • 応用数学、統計数学

  • 数学基礎

研究キーワード

  • 数理統計学

  • 確率論

  • データ科学

  • マルチンゲール

  • 確率場

論文

  • 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年10月  [査読有り]

  • Moment convergence of $Z$-estimators

    Ilia Negri, Yoichi Nishiyama

    STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES   20 ( 3 ) 387 - 397  2017年10月  [査読有り]

     概要を見る

    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年06月  [査読有り]

    DOI CiNii

  • $Z$-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年06月  [査読有り]

    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年02月  [査読有り]

    DOI

  • On $L_2$ space approach to change point problems

    Koji Tsukuda, Yoichi Nishiyama

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   149   46 - 59  2014年06月  [査読有り]

    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年10月  [査読有り]

     概要を見る

    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年10月  [査読有り]

     概要を見る

    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 ( 1 ) 215 - 218  2012年06月  [査読有り]

    CiNii

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

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   41 ( 1 ) 67 - 73  2011年09月  [査読有り]

     概要を見る

    We consider <var>k</var>-sample and change point problems for independent data in a unified way. We propose a test statistic based on the rank statisitcs. The asymptotic distribution under the null hypothesis is shown to be the supremum of the 2-dimensional standard Brownian pillow. Also, the test is shown to be consistent under the alternative that <var>k</var> distribution functions are linearly independent. It is important from practical point of view that our test is not only asymptotically distribution free but also distribution free even for fixed finite sample.

    DOI CiNii

  • 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年04月  [査読有り]

     概要を見る

    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年  [査読有り]

     概要を見る

    Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t(0)(n) &lt; t(1)(n) &lt; ... &lt; t(n)(n) such that t(n)(n) -&gt; infinity and n Delta(1+ p)(n) -&gt; 0, where Delta(n) = max(1 &lt;= i &lt;= 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年  [査読有り]

     概要を見る

    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年  [査読有り]

    DOI

  • On $Z$-estimation by rounded data

    Yoichi Nishiyama

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   141 ( 1 ) 287 - 292  2011年01月  [査読有り]

    DOI

  • Moment convergence of $M$-estimators

    Yoichi Nishiyama

    STATISTICA NEERLANDICA   64 ( 4 ) 505 - 507  2010年11月  [査読有り]

    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年10月  [査読有り]

     概要を見る

    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年04月  [査読有り]

     概要を見る

    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年02月  [査読有り]

     概要を見る

    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

  • 平滑化 Nelson-Aalen 推定量の一様収束率

    西山 陽一

    統計数理   58 ( 1 ) 131 - 135  2010年  [査読有り]

     概要を見る

    要旨あり研究ノート

    CiNii

  • 射影推定量についての一注意

    西山 陽一

    統計数理   58 ( 1 ) 127 - 130  2010年  [査読有り]

     概要を見る

    要旨あり研究ノート

    CiNii

  • 観測ノイズが極値分布に影響を与えないための十分条件

    西山 陽一, 志村 隆彰

    統計数理   57 ( 2 ) 443 - 447  2009年12月  [査読有り]

     概要を見る

    要旨あり研究ノート

    CiNii

  • Two sample problem for rounded data

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   39   233 - 238  2009年12月  [査読有り]

    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年12月  [査読有り]

    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年12月  [査読有り]

     概要を見る

    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年11月  [査読有り]

     概要を見る

    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

  • 拡散過程のノンパラメトリック適合度検定

    西山 陽一

    統計数理   57 ( 1 ) 83 - 95  2009年06月  [査読有り]

     概要を見る

    要旨あり確率過程の統計解析研究ノート

    CiNii

  • Donsker's theorem for discretized data

    Yoichi Nishiyama

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY   38 ( 3 ) 505 - 515  2008年12月  [査読有り]

     概要を見る

    In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory to obtain a (right) Kolmogorov-Smirnov test for discretized data.

    DOI CiNii

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

    Yoichi Nishiyama

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   118 ( 6 ) 1043 - 1055  2008年06月  [査読有り]

     概要を見る

    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年05月  [査読有り]

    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年06月  [査読有り]

    担当区分:責任著者

     概要を見る

    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年04月  [査読有り]

  • 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年04月  [査読有り]

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

    Yoichi Nishiyama

    PROBABILITY THEORY AND RELATED FIELDS   108 ( 4 ) 459 - 494  1997年08月  [査読有り]

  • 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年06月  [査読有り]

     概要を見る

    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.

▼全件表示

書籍等出版物

  • Martingale Methods in Statistics

    Yoichi Nishiyama

    CRC Press, Taylor & Francis Group  2022年 ISBN: 9781466582811

  • マルチンゲール理論による統計解析

    西山 陽一

    近代科学社  2011年10月

  • Entropy Methods for Martingales

    Yoichi Nishiyama

    CWI Tracts  2000年

Misc

受賞

  • 第23回日本統計学会小川研究奨励賞

    2009年09月   日本統計学会  

    受賞者: 西山 陽一

共同研究・競争的資金等の研究課題

  • 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)

    研究期間:

    2018年04月
    -
    2023年03月
     

    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)

    研究期間:

    2015年04月
    -
    2018年03月
     

    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)

    研究期間:

    2012年04月
    -
    2015年03月
     

    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)

    研究期間:

    2009年04月
    -
    2012年03月
     

    西山 陽一

講演・口頭発表等

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

    西山 陽一  [招待有り]

    日本数学会 2013 年度秋季総合分科会  

    発表年月: 2013年09月

  • Adaptive semiparametric estimation for diffusion processes

    Yoichi Nishiyama  [招待有り]

    The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting  

    発表年月: 2012年07月

  • Bracketing CLT for martingales

    Yoichi Nishiyama  [招待有り]

    52th ISI World Statistical Congress  

    発表年月: 1999年08月

  • 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  [招待有り]

    日本数学会 1999 年度年会  

    発表年月: 1999年03月

 

現在担当している科目

▼全件表示

担当経験のある科目(授業)

  • 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  

▼全件表示

 

委員歴

  • 2013年
    -
    2015年

    日本統計学会  会誌編集理事(欧文)

  • 2010年
    -
    2012年

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

  • 2009年
    -
    2010年

    日本数学会  評議員

  • 2007年
    -
    2009年

    日本数学会  和文誌「数学」編集委員

  • 2007年
    -
    2008年

    統計学関連連合大会  企画委員