A study on estimation of restricted parameters and its applications

• Project/Area Number: 20500260
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Toho University
• Principal Investigator: TSUKUMA Hisayuki Toho University, 医学部, 講師 (50424685)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 統計的推測 / ベイズ推定 / 統計的決定理論 / 縮小推定 / スタイン現象 / 多変量推測理論 / 縮小型推定 / 指数型分布族 / 楕円型分布族 / 位置母数

Research Abstract

This research addresses the problem of estimating restricted parameters from a decision-theoretic point of view. We propose new shrinkage estimators and generalized Bayes estimators which lie in the restricted action space, and discuss the minimaxity of the proposed estimators by analytical evaluation of their risk functions. Monte Carlo simulations show the proposed estimators have better risk performance than some estimators studied in the literature.

Research Products

• [Journal Article] Modifying estimators of ordered positive parameters under the Stein loss (2011)
  • Author(s): Tsukuma H., Kubokawa T.
  • Journal Title: Journal of Multivariate Analysis 102 Pages: 164-181
  • Peer Reviewed
• [Journal Article] Proper Bayes minimax estimators of the normal mean matrix with common unknown variances (2010)
  • Author(s): Tsukuma H.
  • Journal Title: Journal of Statistical Planning and Inference 140 Pages: 2596-2606
  • Peer Reviewed
• [Journal Article] Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution (2010)
  • Author(s): Tsukuma H.
  • Journal Title: Journal of Multivariate Analysis 101 Pages: 1483-1492
  • Peer Reviewed
• [Journal Article] Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution (2010)
  • Author(s): Tsukuma H.
  • Journal Title: Statistics & Probability Letters 80 Pages: 215-220
  • Peer Reviewed
• [Journal Article] Proper Bayes minimax estimators of the normal mean matrix with common unknown variances (2010)
  • Author(s): Tsukuma, H.
  • Journal Title: Journal of Statistical Planning and Inference. Volume: 140 Pages: 2599-2606
  • Peer Reviewed
• [Journal Article] Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution (2010)
  • Author(s): Tsukuma, H.
  • Journal Title: Journal of Multivariate Analysis Volume: 101 Pages: 1483-1492
  • Peer Reviewed
• [Journal Article] Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution (2010)
  • Author(s): Tsukuma, H.
  • Journal Title: Statistics & Probability Letters Volume: 80 Pages: 215-220
  • Peer Reviewed
• [Journal Article] Shrinkage estimation in elliptically contoured distribution with restricted parameter space (2009)
  • Author(s): Tsukuma H.
  • Journal Title: Statistics & Decisions 27 Pages: 25-35
  • Peer Reviewed
• [Journal Article] Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix (2009)
  • Author(s): Tsukuma H.
  • Journal Title: Journal of Multivariate Analysis 100 Pages: 2296-2304
  • Peer Reviewed
• [Journal Article] Minimax estimation of normal precisions via expansion estimators (2009)
  • Author(s): Tsukuma H., Kubokawa T.
  • Journal Title: Journal of Statistical Planning and Inference 139 Pages: 295-309
  • Peer Reviewed
• [Journal Article] Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix (2009)
  • Author(s): Tsukuma, H.
  • Journal Title: Journal of Multivariate Analysis 100 Pages: 2296-2304
  • Peer Reviewed
• [Journal Article] Shrinkage estimation in elliptically contoured distribution with restricted parameter space (2009)
  • Author(s): Tsukuma, H.
  • Journal Title: Statistics & Decisions 27 Pages: 25-35
  • Peer Reviewed
• [Journal Article] Minimax estimation of normal precisions via expansion estimators (2009)
  • Author(s): Tsukuma, H., Kubokawa, T.
  • Journal Title: Journal of Statistical Planning and Inference 139 Pages: 295-309
  • Peer Reviewed
• [Journal Article] Minimaxity of the Stein risk-minimization estimator for a normal mean matrix (2008)
  • Author(s): Kubokawa T., Tsukuma H.
  • Journal Title: Statistics & Decisions 26 Pages: 243-261
  • Peer Reviewed
• [Journal Article] Admissibility and minimaxity of Bayes estimators for a normal mean matrix (2008)
  • Author(s): Tsukuma H.
  • Journal Title: Journal of Multivariate Analysis 99 Pages: 2251-2264
  • Peer Reviewed
• [Journal Article] Stein' s phenomenon in estimation of means restricted to a polyhedral convex cone (2008)
  • Author(s): H. Tsukuma, T. Kubokawa
  • Journal Title: Journal of Multivariate Analysis 99 Pages: 141-164
  • Peer Reviewed
• [Journal Article] Admissibility and minimaxity of Bayes estimators for a normal mean matrix (2008)
  • Author(s): H. Tsukuma
  • Journal Title: Journal of Multivariate Analysis 99 Pages: 2251-2264
  • Peer Reviewed
• [Remarks] 研究代表者のホームページ
  • URL: http://www.lab.toho-u.ac.jp/med/minfo/tsukuma/