The Annals of Statistics

Inadmissibility Results for the Selected Scale Parameters

P. Vellaisamy

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Abstract

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.

Article information

Source
Ann. Statist., Volume 20, Number 4 (1992), 2183-2191.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348913

Digital Object Identifier
doi:10.1214/aos/1176348913

Mathematical Reviews number (MathSciNet)
MR1193336

Zentralblatt MATH identifier
0765.62012

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62F07: Ranking and selection

Keywords
Estimation after selection gamma scale parameters inadmissible estimators differential inequalities simultaneous estimation after selection

Citation

Vellaisamy, P. Inadmissibility Results for the Selected Scale Parameters. Ann. Statist. 20 (1992), no. 4, 2183--2191. doi:10.1214/aos/1176348913. https://projecteuclid.org/euclid.aos/1176348913


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