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SCRA 2002-FIM IX: Ninth International Conference of Forum for Interdisciplinary Mathematics on Statistics Combinatorics and Related Areas
December 21-23, 2002
Department of Statistics and Department of Mathematics: University of Allahabad
Allahabad, UP, India

Organizers
Satya Mishra, Anoop Chaturvedi, Bhu Dev Sharma

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On Estimating the Scale Parameter of the Selected Gamma Population Under the Scale Invariant Squared Error Loss Function
by
Neeraj Misra
Indian Institute of Technology Kanpur
Coauthors: E.C. Van der Meulen (Katholieke University, Leuven, Belgium), Karlien V Branden (Katholieke University, Leuven, Belgium)

On Estimating the Scale Parameter of the Selected Gamma Population Under the Scale Invariant Squared Error Loss Function

On Estimating the Scale Parameter of the Selected Gamma Population Under the Scale Invariant Squared Error Loss Function

Neeraj Misra
Department of Mathematics
Indian Institute of Technology Kanpur
Kanpur 208 016
INDIA, Edward C. van der Meulen & Karlien Vanden Branden
Department of Mathematics
Katholieke University Leuven
B-3001 Heverlee
BELGIUM

Abstract

Let X1 and X2 be two independent random variables representing the populations \Pi1 and \Pi2, respectively, and suppose that the random variable Xi has a gamma distribution with shape parameter p, same for both the populations, and unknown scale parameter \thetai,  i=1, 2. Define, M=1, if X1 > X2,  M = 2, if X2 > X1 and J=3-M. We consider the component wise estimation of random parameters \thetaM and \thetaJ, under the scale invariant squared error loss functions L1(\theta, \delta1)=([(\delta1)/(\thetaM)]-1)2 and L2(\theta, \delta2)=([(\delta2)/(\thetaJ)]-1)2, respectively. Sufficient conditions for the inadmissibility of equivariant estimators of \thetaM and \thetaJ are derived. As a consequence, various natural estimators are shown to be inadmissible and better estimators are obtained.

Date received: November 20, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakd-30.