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December, 1992 Inadmissibility Results for the Selected Scale Parameters
P. Vellaisamy
Ann. Statist. 20(4): 2183-2191 (December, 1992). DOI: 10.1214/aos/1176348913


Let $X_1, X_2, \ldots, X_k$ be $k$ independent gamma random variables with different scale parameters but with a common known shape parameter. Suppose the population corresponding to the largest $X_{(1)}$ [or the smallest $X_{(k)}$] observation is selected. The problem of estimating the scale parameter $\theta_{(1)}$ [or $\theta_{(k)}$] of the selected population is considered. We derive, using the method of differential inequalities, explicit estimators that dominate the natural or the existing estimators. The improved estimators of $\theta_{(1)}$ are similar to that of DasGupta estimators for the usual simultaneous estimation problem. An implication of this result for the simultaneous estimation of the selected subset is also considered.


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P. Vellaisamy. "Inadmissibility Results for the Selected Scale Parameters." Ann. Statist. 20 (4) 2183 - 2191, December, 1992.


Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62012
MathSciNet: MR1193336
Digital Object Identifier: 10.1214/aos/1176348913

Primary: 62C15
Secondary: 62F07, 62F10

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 4 • December, 1992
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