A study on statistical inference based on singular Wishart matrices and its applications

• Project/Area Number: 15K00055
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Toho University
• Principal Investigator: TSUKUMA Hisayuki 東邦大学, 医学部, 准教授 (50424685)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 多変量推測統計 / 統計的決定理論 / スタイン現象 / 縮小型推定 / ベイズ推定 / 高次元モデル / カルバック・ライブラー情報量 / 多変量推測理論

Outline of Final Research Achievements

This study addressed a high-dimensional normal distribution model with small sample size and considered shrinkage estimation based on singular Wishart matrices from a decision-theoretic point of view. Some new estimators of covariance matrix were proposed under a Stein-type loss. Also, this study considered the problem of estimating predictive densities related to estimation of a normal mean matrix, and succeeded in deriving proper Bayes minimax predictive densities relative to the Kullback-Leibler loss.

Research Products

• [Journal Article] Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix (2017)
  • Author(s): Hisayuki Tsukuma, Tatsuya Kubokawa
  • Journal Title: Journal of Multivariate Analysis Volume: 159 Pages: 138-150
  • DOI: 10.1016/j.jmva.2017.05.004
  • Peer Reviewed
• [Journal Article] Unified improvements in estimation of a normal covariance matrix in high and low dimensions (2016)
  • Author(s): Tsukuma, H. and Kubokawa, T.
  • Journal Title: Journal of Multivariate Analysis Volume: 143 Pages: 233-248
  • DOI: 10.1016/j.jmva.2015.09.016
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition (2016)
  • Author(s): Tsukuma, H.
  • Journal Title: Journal of Multivariate Analysis Volume: 145 Pages: 190-207
  • DOI: 10.1016/j.jmva.2015.12.013
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Estimation of a high-dimensional covariance matrix with the Stein loss (2016)
  • Author(s): Tsukuma, H.
  • Journal Title: Journal of Multivariate Analysis Volume: 148 Pages: 1-17
  • DOI: 10.1016/j.jmva.2016.02.012
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Estimation of the mean vector in a singular multivariate normal distribution (2015)
  • Author(s): Tsukuma, H. and Kubokawa, T.
  • Journal Title: Journal of Multivariate Analysis Volume: 140 Pages: 245-258
  • DOI: 10.1016/j.jmva.2015.05.016
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A unified approach to estimating a normal mean matrix in high and low dimensions (2015)
  • Author(s): Tsukuma, H. and Kubokawa, T.
  • Journal Title: Journal of Multivariate Analysis Volume: 139 Pages: 312-328
  • DOI: 10.1016/j.jmva.2015.04.003
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Minimaxity in estimation of restricted and non-restricted scale parameter matrices (2015)
  • Author(s): Tsukuma, H. and Kubokawa, T.
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 67 Issue: 2 Pages: 261-285
  • DOI: 10.1007/s10463-014-0449-x
  • NAID: 40020387949
  • Peer Reviewed