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March, 1989 All Admissible Linear Estimators of the Vector of Gamma Scale Parameters with Application to Random Effects Models
Roger H. Farrell, Witold Klonecki, Stefan Zontek
Ann. Statist. 17(1): 268-281 (March, 1989). DOI: 10.1214/aos/1176347015

Abstract

The paper is devoted to the problem of simultaneous estimation of scale and natural parameters of the multiparameter gamma distribution under a quadratic loss. The vector of the scale parameters is assumed to range over a certain subset of the Cartesian product $\mathscr{R}^n_+$ of $n$ positive half lines. We identify the class of all linear admissible estimators for the scale parameters and show that all linear estimators of the natural parameters are inadmissible. Since the problem of invariant quadratic estimation of variance components in balanced random effects normal models leads to a problem of linear estimation of parametric functions of gamma scale parameters restricted to subsets of $\mathscr{R}^n_+$ being considered in this paper, some results on admissibility of invariant quadratic estimators of variance components are also established.

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Roger H. Farrell. Witold Klonecki. Stefan Zontek. "All Admissible Linear Estimators of the Vector of Gamma Scale Parameters with Application to Random Effects Models." Ann. Statist. 17 (1) 268 - 281, March, 1989. https://doi.org/10.1214/aos/1176347015

Information

Published: March, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0671.62014
MathSciNet: MR981449
Digital Object Identifier: 10.1214/aos/1176347015

Subjects:
Primary: 62C15
Secondary: 62F10

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • March, 1989
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