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

[41] A FAMILY OF DOMINATING MINIMAX ESTIMATORS OF A MULTIVARIATE NORMAL-MEAN
LI, TF
STATISTICS & PROBABILITY LETTERS, 1984, 2 (04) : 215 - 217
[42] FAMILY OF ADMISSIBLE MINIMAX ESTIMATORS OF MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION
ALAM, K
ANNALS OF STATISTICS, 1973, 1 (03): : 517 - 525
[43] On combining correlated estimators of the common mean of a multivariate normal distribution
Krishnamoorthy, K
Lu, Y
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2005, 75 (05) : 333 - 345
[44] Set-induced minimax estimators for a multivariate normal mean
Tseng, YL
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2004, 121 (01) : 53 - 64
[45] MINIMAX ESTIMATION OF THE MEAN OF SPHERICALLY SYMMETRIC DISTRIBUTIONS UNDER GENERAL QUADRATIC LOSS
BRANDWEIN, AC
JOURNAL OF MULTIVARIATE ANALYSIS, 1979, 9 (04) : 579 - 588
[46] GENERAL CLASSES OF SHRINKAGE ESTIMATORS FOR THE MULTIVARIATE NORMAL MEAN WITH UNKNOWN VARIANCE: MINIMAXITY AND LIMIT OF RISKS RATIOS
Benkhaled, Abdelkader
Hamdaoui, Abdenour
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2022, 46 (02): : 193 - 213
[47] Bayesian multivariate normal analysis under the extended reflected normal loss function
Towhidi, M
Behboodian, J
STATISTICS, 2001, 35 (03) : 215 - 223
[48] COMPARISONS OF THE PERFORMANCES OF ESTIMATORS OF A BOUNDED NORMAL MEAN UNDER SQUARED-ERROR LOSS
Dou, Yiping
Van Eeden, Constance
REVSTAT-STATISTICAL JOURNAL, 2009, 7 (03) : 203 - +
[49] A class of general pretest estimators for the univariate normal mean
Shih, Jia-Han
Konno, Yoshihiko
Chang, Yuan-Tsung
Emura, Takeshi
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2023, 52 (08) : 2538 - 2561
[50] GENERALIZED BAYES SURE FOR MULTIVARIATE NORMAL DISTRIBUTION UNDER BALANCED-QUADRATIC LOSS
Karamikabir H.
Afshari M.
Karamikabir N.
Kiaei S.F.
Journal of Mathematical Sciences, 2024, 280 (2) : 262 - 274

← 1 2 3 4 5 →