An extended class of minimax generalized Bayes estimators of regression coefficients

被引：4

作者：

Maruyama, Yuzo ^{[1
]}

Strawderman, William E. ^{[2
]}

机构：

[1] Univ Tokyo, Ctr Spatial Informat Sci, Tokyo 1130033, Japan

[2] Rutgers State Univ, Piscataway, NJ 08855 USA

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2009年 / 100卷 / 10期

关键词：

Regression; Minimaxity; Shrinkage estimators; Generalized Bayes estimators; Invariant loss; Unknown variance; Hypergeometric function; MULTIVARIATE NORMAL-DISTRIBUTION;

D O I：

10.1016/j.jmva.2009.06.001

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：

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753-1770] to include non-monotone shrinkage functions. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2155 / 2166

页数：12

共 11 条

[1] FAMILY OF ADMISSIBLE MINIMAX ESTIMATORS OF MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION [J].

ALAM, K .

ANNALS OF STATISTICS, 1973, 1 (03) :517-525

[2]

[Anonymous], 1964, HDB MATH FUNCTIONS

[3]

[Anonymous], 1994, The Bayesian Choice

[4] FAMILIES OF MINIMAX ESTIMATORS OF MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION [J].

EFRON, B ;

MORRIS, C .

ANNALS OF STATISTICS, 1976, 4 (01) :11-21

[5] Robust improvement in estimation of a mean matrix in an elliptically contoured distribution [J].

Kubokawa, T ;

Srivastava, MS .

JOURNAL OF MULTIVARIATE ANALYSIS, 2001, 76 (01) :138-152

[6] A new class of generalized Bayes minimax ridge regression estimators [J].

Maruyama, Y ;

Strawderman, WE .

ANNALS OF STATISTICS, 2005, 33 (04) :1753-1770

[7] A unified and broadened class of admissible minimax estimators of a multivariate normal mean [J].

Maruyama, Y .

JOURNAL OF MULTIVARIATE ANALYSIS, 1998, 64 (02) :196-205

[8] Stein's idea and minimax admissible estimation of a multivariate normal mean [J].

Maruyama, Y .

JOURNAL OF MULTIVARIATE ANALYSIS, 2004, 88 (02) :320-334

[9]

Maruyama Y., 2003, Statistics and Decisions, V21, P69, DOI DOI 10.1524/STND.21.1.69

[10]

Stein C., 1973, P PRAG S AS STAT, P345

← 1 2 →