Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function

被引：1

作者：

Hamdaoui, Abdenour ^{[1
,2
]}

Benkhaled, Abdelkader ^{[3
]}

Terbeche, Mekki ^{[1
,4
]}

机构：

[1] Univ Sci & Technol Mohamed Boudiaf, Dept Math, Oran, Algeria

[2] Lab Stat & Random Modelisat LSMA, Tilimsen, Algeria

[3] Mascara Univ Mustapha Stambouli, Lab Geomat Ecol & Environm LGEO2E, Dept Biol, Mascara, Algeria

[4] USTO MB, Lab Anal & Applicat Radiat LAAR, Oran, Algeria

来源：

JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS | 2020年 / 13卷 / 05期

关键词：

covariance matrix; James-Stein estimator; loss function; multivariate gaussian random variable; non-central chi-square distribution; shrinkage estimator; MINIMAX ESTIMATORS; FAMILY;

D O I：

10.17516/1997-1397-2020-13-5-608-621

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular the class of James-Stein estimator is presented. The general situation for both matrices cited above is discussed.

引用

页码：608 / 621

页数：14

共 50 条

[21] MINIMAX ESTIMATE FOR MEAN OF A NORMAL RANDOM VECTOR UNDER A GENERALIZED QUADRATIC LOSS FUNCTION
BASAR, T
MINTZ, M
ANNALS OF STATISTICS, 1973, 1 (01): : 127 - 134
[22] Bayes minimax estimation of the multivariate normal mean vector under balanced loss function
Zinodiny, S.
Rezaei, S.
Nadarajah, S.
STATISTICS & PROBABILITY LETTERS, 2014, 93 : 96 - 101
[23] MINIMAX ESTIMATORS FOR MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION
TSAI, HL
LIN, PE
ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (05): : 1804 - &
[24] Polynomials shrinkage estimators of a multivariate normal mean
Benkhaled, Abdelkader
Terbeche, Mekki
Hamdaoui, Abdenour
arXiv, 2021,
[25] MINIMAX ESTIMATORS OF MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION
BOCK, ME
ANNALS OF STATISTICS, 1975, 3 (01): : 209 - 218
[26] MINIMAX BAYES ESTIMATORS OF A MULTIVARIATE NORMAL MEAN
FAITH, RE
JOURNAL OF MULTIVARIATE ANALYSIS, 1978, 8 (03) : 372 - 379
[27] Φ admissibility for linear estimators on regression coefficients in a general multivariate linear model under balanced loss function
Cao, Mingxiang
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2009, 139 (09) : 3354 - 3360
[28] MINIMAX ESTIMATION OF A MULTIVARIATE NORMAL MEAN UNDER POLYNOMIAL LOSS
BERGER, JO
JOURNAL OF MULTIVARIATE ANALYSIS, 1978, 8 (02) : 173 - 180
[29] Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function
Cao, Ming-Xiang
He, Dao-Jiang
JOURNAL OF MULTIVARIATE ANALYSIS, 2017, 153 : 246 - 254
[30] SHRINKAGE ESTIMATORS WITH GENERAL QUADRATIC LOSS AND SHRINKAGE FUNCTION WHICH IS NOT NECESSARILY CONTINUOUS
CELLIER, D
FOURDRINIER, D
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1986, 302 (18): : 665 - 668

← 1 2 3 4 5 →