James-Stein estimators for the mean vector of a multivariate normal population based on independent samples from two normal populations with common covariance structure

Khan, Shahjahan and Hoque, Zahirul (2002) James-Stein estimators for the mean vector of a multivariate normal population based on independent samples from two normal populations with common covariance structure. Pakistan Journal of Statistics, 18 (3). pp. 359-381. ISSN 1012-9367

[img]
Preview
PDF (Author version)
Khan_Haque_2002_authorversion.pdf

Download (179Kb)

Abstract

The paper considers shrinkage estimators of the mean vector of a multivariate normal population based on independent random samples from two multivariate normal populations with different mean vectors but common covariance structure. The shrinkage and the positive-rule shrinkage estimators are defined by using the preliminary test approach when uncertain prior information regarding the equality of the two population mean vectors is available. The properties and performances of the estimators are investigated. The performances of the estimators are compared based on the unbiasedness and quadratic risk criteria. The relative performances of the estimators are discussed under different conditions. The shrinkage estimator dominates the maximum likelihood estimator, and the positive-rule shrinkage estimator uniformly over performs the shrinkage estimator with respect to the quadratic risk.


Statistics for USQ ePrint 2644
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited with blanket permission of publisher. Access the publisher version at: http://www.pakjs.com/journals/18(3)/18(3)2.pdf
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 01:11
Last Modified: 02 Jul 2013 22:45
Uncontrolled Keywords: two-sample problem; uncertain prior information; preliminary test approach; multivariate normal; noncentral chi-square and F-distributions; incomplete beta ratio; bias and quadratic bias; quadratic risk; admissibility
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
URI: http://eprints.usq.edu.au/id/eprint/2644

Actions (login required)

View Item Archive Repository Staff Only