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.

引用

页码：313 / 328

页数：16

共 50 条

[1] ORTHOGONALLY INVARIANT ESTIMATION OF THE SKEW-SYMMETRICAL NORMAL-MEAN MATRIX
KURIKI, S
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1993, 45 (04) : 731 - 739
[2] Admissibility and minimaxity of Bayes estimators for a normal mean matrix
Tsukuma, Hisayuki
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2008, 99 (10) : 2251 - 2264
[3] MINIMAX ESTIMATORS OF A NORMAL-MEAN VECTOR FOR ARBITRARY QUADRATIC LOSS AND UNKNOWN COVARIANCE-MATRIX
GLESER, LJ
[J]. ANNALS OF STATISTICS, 1986, 14 (04): : 1625 - 1633
[4] A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution
Zinodiny, Shokofeh
Nadarajah, Saralees
[J]. MATHEMATICS, 2024, 12 (07)
[5] THE EUCLIDEAN DISTANCE DEGREE OF ORTHOGONALLY INVARIANT MATRIX VARIETIES
Drusvyatskiy, Dmitriy
Lee, Hon-Leung
Ottaviani, Giorgio
Thomas, Rekha R.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2017, 221 (01) : 291 - 316
[6] The euclidean distance degree of orthogonally invariant matrix varieties
Dmitriy Drusvyatskiy
Hon-Leung Lee
Giorgio Ottaviani
Rekha R. Thomas
[J]. Israel Journal of Mathematics, 2017, 221 : 291 - 316
[7] INADMISSIBILITY OF NON-ORDER-PRESERVING ORTHOGONALLY INVARIANT ESTIMATORS OF THE COVARIANCE-MATRIX IN THE CASE OF STEIN LOSS
SHEENA, Y
TAKEMURA, A
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1992, 41 (01) : 117 - 131
[8] Proper Bayes minimax estimators of the normal mean matrix with common unknown variances
Tsukuma, Hisayuki
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (09) : 2596 - 2606
[9] GENERALIZED BAYES MINIMAX ESTIMATORS OF MULTIVARIATE NORMAL MEAN WITH UNKNOWN COVARIANCE MATRIX
LIN, P
TSAI, H
[J]. ANNALS OF STATISTICS, 1973, 1 (01): : 142 - 145
[10] Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method
Chen, Xiang
Huang, Minyi
[J]. 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2018, : 4117 - 4122

← 1 2 3 4 5 →