Improved estimation of the mean vector for Student-t model.

Khan, Shahjahan (2000) Improved estimation of the mean vector for Student-t model. Communications In Statistics: Theory & Methods, 29 (3). pp. 507-527. ISSN 0361-0926

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Abstract

Improved James-Stein type estimation of the mean vector $\mbox{\boldmath $\mu$}$ of a multivariate Student-t 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), Stein-type shrinkage estimator (SE) and positive-rule 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, James-Stein estimator, preliminary test and shrinkage estimator, bias, quadratic risk, multivariate normal, Student-t 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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