Khan, Shahjahan (2000) Improved estimation of the mean vector for Studentt model. Communications In Statistics: Theory & Methods, 29 (3). pp. 507527. ISSN 03610926

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Abstract
Improved JamesStein type estimation of the mean vector $\mbox{\boldmath $\mu$}$ of a multivariate Studentt population of dimension p with $\nu$ degrees of freedom is considered. In addition to the sample data, uncertain prior information on the value of the mean vector, in the form of a null hypothesis, is used for the estimation. The usual maximum likelihood estimator (mle) of $\mbox{\boldmath $\mu$}$ is obtained and a test statistic for testing $H_0: \mbox{\boldmath $\mu$} = \mbox{\boldmath $\mu$}_0$ is derived. Based on the mle of $\mbox{\boldmath $\mu$}$ and the test statistic the preliminary test estimator (PTE), Steintype shrinkage estimator (SE) and positiverule shrinkage estimator (PRSE) are defined. The bias and the quadratic risk of the estimators are evaluated. The relative performances of the estimators are investigated by analyzing the risks under different conditions. It is observed that the PRSE dominates over the other three estimators, regardless of the validity of the null hypothesis and the value $\nu.$
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Item Type:  Article (Commonwealth Reporting Category C) 

Refereed:  Yes 
Item Status:  Live Archive 
Additional Information:  Deposited in accordance with the copyright requirements of the publisher. 
Depositing User:  Professor Shahjahan Khan 
Faculty / Department / School:  Historic  Faculty of Sciences  Department of Maths and Computing 
Date Deposited:  11 Oct 2007 00:34 
Last Modified:  02 Jul 2013 22:35 
Uncontrolled Keywords:  uncertain prior information, maximum likelihood estimator, likelihood ratio test, JamesStein estimator, preliminary test and shrinkage estimator, bias, quadratic risk, multivariate normal, Studentt and inverted gamma distributions, dominance, and relative efficiency 
Fields of Research (FOR2008):  01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory 
URI:  http://eprints.usq.edu.au/id/eprint/1052 
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