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A note on second-order admissibility of the Graybill-Deal estimator of a common mean of several normal populations

โœ Scribed by Nabendu Pal; Wooi K. Lim

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
295 KB
Volume
63
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

Consider the problem of estimating the common mean of several normal populations with unknown and possibly unequal variances under the squared error loss function. The well-known unbiased estimator of the common mean is the Graybill-Deal estimator. The general admissibility (or otherwise) of this estimator is still an open problem even though Sinha and Mouqadem (Comm. Statist. Theory Methods 11 (1982) 1603-1614) proved some restricted admissibility results. In this paper, we follow the asymptotic decision-theoretic approach of "second-order admissibility' as adopted by Ghosh and Sinha (Ann. Statist. 9 (1981) 1334-1338), and prove that the GraybiU-Deal estimator is second-order admissible.

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