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

2017 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

数理統計学