Matrix quadratic risk of orthogonally invariant estimators for a normal mean matrix

被引：0
|
作者：
Matsuda, Takeru [1 ,2 ]
机构：
[1] Univ Tokyo, Grad Sch Informat Sci & Technol, 7-3-1 Hongo,Bunkyo Ku, Tokyo 1138656, Japan
[2] RIKEN, RIKEN Ctr Brain Sci, 2-1 Hirosawa, Wako, Saitama 3510198, Japan
来源：
JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE | 2024年 / 7卷 / 01期
关键词：
Efron-Morris estimator; Matrix; Shrinkage; Singular value; Stein estimation; BAYES;
D O I：
10.1007/s42081-023-00216-z
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In estimation of a normal mean matrix under the matrix quadratic loss, we develop a general formula for the matrix quadratic risk of orthogonally invariant estimators. The derivation is based on several formulas for matrix derivatives of orthogonally invariant functions of matrices. As an application, we calculate the matrix quadratic risk of a singular value shrinkage estimator motivated by Stein's proposal for improving on the Efron-Morris estimator 50 years ago.
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页码：313 / 328
页数：16
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