On the comparison of the pre-test and shrinkage estimators for the univariate normal mean

Khan, Shahjahan and Saleh, A. K. Md. E. (2001) On the comparison of the pre-test and shrinkage estimators for the univariate normal mean. Statistical Papers, 42 (4). pp. 451-473. ISSN 0932-5026

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Abstract

The estimation of the mean of an univariate normal population with unknown variance is considered when uncertain non-sample prior information is available. Alternative estimators are defined to incorporate both the sample as well as the non-sample information in the estimation process. Some of the important statistical properties of the restricted, preliminary test, and shrinkage estimators are investigated. The performances of the estimators are compared based on the criteria of unbiasedness and mean square error in order to search for a 'best' estimator. Both analytical and graphical methods are explored. There is no superior estimator that uniformly dominates the others. However, if the non-sample information regarding the value of the mean is close to its true value, the shrinkage estimator over performs the rest of the estimators.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version deposited in accordance with the copyright policy of the publisher. Copyright 2001 Springer. This is the author's version of the work. It is posted here with permission of the publisher for your personal use. No further distribution is permitted. The original publication is available at: http://www.springerlink.comPre-print version of article, as made available ehre, differs in title from the Published version. Pre-print title: On the comparison of the pre-test and Stein-type estimators for the univariate normal mean.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:33
Last Modified: 02 Jul 2013 22:35
Uncontrolled Keywords: uncertain non-sample prior information; maximum likelihood; restricted; preliminary test and shrinkage estimators; bias; mean square error; relative efficiency; normal; student; non-central chi-square and F distributions; incomplete beta ratio
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/1051

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