Minimax estimator of regression coefficient in normal distribution under balanced loss function

被引：2

作者：

Hu, Guikai ^{[1
,2
]}

Li, Qingguo ^{[1
]}

Peng, Ping ^{[2
]}

机构：

[1] Hunan Univ, Sch Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] E China Inst Technol, Sch Sci, Fuzhou 344000, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 05期

关键词：

Balanced loss function; Normal distribution; Regression coefficient; Minimax estimator; MULTIVARIATE NORMAL-DISTRIBUTION; LINEAR ESTIMATORS; ADMISSIBILITY; MODEL;

D O I：

10.1016/j.laa.2011.08.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article investigates linear minimax estimators of regression coefficient in a linear model with an assumption that the underlying distribution is a normal one with a nonnegative definite covariance matrix under a balanced loss function. Some linear minimax estimators of regression coefficient in the class of all estimators are obtained. The result shows that the linear minimax estimators are unique under some conditions. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1228 / 1237

页数：10

共 19 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]

Arashi M., 2009, PROBLEM ESTIMATION B

[3] Φ admissibility for linear estimators on regression coefficients in a general multivariate linear model under balanced loss function [J].

Cao, Mingxiang .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2009, 139 (09) :3354-3360

[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] The exact risks of some pre-test and Stein-type regression estimators under balanced loss [J].

Giles, JA ;

Giles, DEA ;

Ohtani, K .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1996, 25 (12) :2901-2924

[6] The efficiency of shrinkage estimators with respect to Zellner's balanced loss function [J].

Gruber, MHJ .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2004, 33 (02) :235-249

[7] Admissibility for linear estimators of regression coefficient in a general Gauss-Markoff model under balanced loss function [J].

Hu, Guikai ;

Peng, Ping .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (11) :3365-3375

[8] On estimation with weighted balanced-type loss function [J].

Jozani, MJ ;

Marchand, É ;

Parsian, A .

STATISTICS & PROBABILITY LETTERS, 2006, 76 (08) :773-780

[9] Inadmissibility of the Stein-rule estimator under the balanced loss function [J].

Ohtani, K .

JOURNAL OF ECONOMETRICS, 1999, 88 (01) :193-201

[10]

Ohtani K., 1997, Econometric Reviews, V16, P119

← 1 2 →