Weak convergence in infinite-dimensional spaces and statistical applications

• Project/Area Number: 24540152
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: NISHIYAMA Yoichi 統計数理研究所, 数理・推論研究系, 准教授 (90270412)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: マルチンゲール / 確率場 / 最大不等式 / 無限次元解析 / 変化点問題 / 推定方程式 / 経験過程 / 弱収束 / 緊密性 / Cox モデル / セミパラメトリック統計 / 国際情報交換 / エントロピー / セミパラメトリック推定

Outline of Final Research Achievements

As an alternative to the well-known methods of chaining and bracketing, a new method to establish a stochastic maximal inequality was studied. We took an approach to reduce the maximum of high-dimensional martingales to that of the one-dimensional martingale as the sum of the original martingales.

Research Products

• [Journal Article] On L2 space approach to change point problems (2014)
  • Author(s): Tsukuda, K. and Nishiyama, Y.
  • Journal Title: Journal of Statistical Planning and Inference Volume: 149 Pages: 46-59
  • DOI: 10.1016/j.jspi.2014.02.007
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Asymptotically distribution free test for parameter change in a diffusion process model. (2012)
  • Author(s): Negri, I. and Nishiyama, Y.
  • Journal Title: Ann. Inst. Statist. Math. Volume: 64 Pages: 911-918
  • NAID: 40019382677
  • Peer Reviewed
• [Journal Article] Some problems in nonparametric inference for the stress release process related to the local time. (2012)
  • Author(s): Fujii, T. and Nishiyama, Y.
  • Journal Title: Ann. Inst. Statist. Math. Volume: 64 Pages: 991-1007
  • NAID: 40019382723
  • Peer Reviewed
• [Journal Article] 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． (2012)
  • Author(s): 西山陽一
  • Journal Title: 統計数理 Volume: 60 Pages: 215-218
  • NAID: 40019434426
  • Peer Reviewed
• [Journal Article] Moment convergence of Z-estimators and Z-process method for change point problems. (2012)
  • Author(s): Negri, I. and Nishiyama, Y.
  • Journal Title: Reseach Memorandum, Inst. Statist. Math. Volume: 1158 Pages: 1-28
• [Presentation] 「狭義可算集合」の概念の導入とその動機 (2014)
  • Author(s): 西山陽一
  • Organizer: 2014年統計関連学会連合大会
  • Place of Presentation: 東京大学本郷キャンパス
  • Year and Date: 2014-09-15
• [Presentation] Semiparametric statistics with infinite-dimensional martingales: bridges between a stochastic maximal inequality and Cox's regression model (2014)
  • Author(s): Nishiyama, Y.
  • Organizer: Symposium on "Stable Process, Semimartingale, Finance & Pension Mathematics"
  • Place of Presentation: 早稲田大学
• [Presentation] A stochastic maximal inequality, weak convergence of infinite-dimensional martingales, and semiparametric statistics
  • Author(s): 西山陽一
  • Organizer: 日本数学会
  • Place of Presentation: 愛媛大学
  • Invited
• [Presentation] Applications of entropy methods to some statistical tests for diffusion processes
  • Author(s): Negri, I. and Nishiyama, Y.
  • Organizer: The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting 2012
  • Place of Presentation: つくば国際会議場
  • Invited
• [Presentation] Adaptive semiparametric estimation for diffusion processes
  • Author(s): Nishiyama, Y.
  • Organizer: The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting 2012
  • Place of Presentation: つくば国際会議場
  • Invited
• [Presentation] Z-推定量のモーメント収束
  • Author(s): 西山陽一
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] 変化点問題のための Z-process 法
  • Author(s): 西山陽一
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] Z-推定量のモーメント収束
  • Author(s): 西山陽一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
• [Presentation] 変化点問題のための Z-process 法
  • Author(s): 西山陽一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
• [Presentation] Martingale methods in statistics
  • Author(s): Nishiyama, Y.
  • Organizer: ISI-ISM-ISSAS Joint Conference
  • Place of Presentation: Academia Sinica, Taipei
  • Invited
• [Presentation] On "Entropy-Martingale Methods in Statistics''
  • Author(s): Nishiyama, Y.
  • Organizer: JAFEE-Columbia-ISM International Conference
  • Place of Presentation: 統計数理研究所
  • Invited