Development on statistical inference for matrix-valued statistics

• Project/Area Number: 25330043
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Japan Women's University
• Principal Investigator: Yoshihiko Konno 日本女子大学, 理学部, 教授 (00205577)
• Research Collaborator: EMURA Takeshi
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: ウィシャート分布 / 行列値統計量 / 統計的決定理論 / 最尤推定量 / 両側切断データ / 行列統計量 / 統計モデル / 縮小推定 / メタアナリシス / 共通平均 / 低ランク行列 / 推定問題 / 検定問題 / 縮小推定量 / 分散共分散行列

Outline of Final Research Achievements

(1) Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm.
(2) Biased sampling affects the inference for population parameters of interest if the sampling mechanism is not appropriately handled. This paper considers doubly-truncated data arising in lifetime data analysis in which samples are subject to both left- and right-truncations. To correct for the sampling bias with doubly-truncated data, maximum likelihood estimator (MLE) has been proposed under a parametric family called the special exponential family (Efron and Petrosian, in J Am Stat Assoc, 1999).

Research Products

• [Journal Article] Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation (2017)
  • Author(s): Emura, Takeshi; Hu, Ya-Hsuan; Konno, Yoshihiko
  • Journal Title: Statist. Papers Volume: 58 Pages: 877-909
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Statistical inference based on the nonparametric maximum likelihood estimator under double-truncation (2015)
  • Author(s): Emura, Takeshi, Yoshihiko Konno, Hirofumi Michimae
  • Journal Title: Lifetime Data Analysis Volume: 21 Issue: 3 Pages: 397-418
  • DOI: 10.1007/s10985-014-9297-5
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Multivariate normal distribution approaches for dependently left-truncated datta (2012)
  • Author(s): Takeshi Emura, Yoshihiko Konno
  • Journal Title: Statistical Paper Volume: 53 Issue: 1 Pages: 133-149
  • DOI: 10.1007/s00362-010-0321-x
  • Peer Reviewed
• [Presentation] Shrinkage estimators for large covariance matrices in multivariate normal distribution (2017)
  • Author(s): Yoshihiko Konno
  • Organizer: ワークショップ「行列解析の展開」
  • Place of Presentation: 名古屋大学
  • Invited
• [Remarks] List of Papers
  • URL: http://mcm-www.jwu.ac.jp/~konno/list.html