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March, 1986 Simultaneous Estimation in the Multiparameter Gamma Distribution Under Weighted Quadratic Losses
Anirban Das Gupta
Ann. Statist. 14(1): 206-219 (March, 1986). DOI: 10.1214/aos/1176349850


A new class of solutions to a general differential inequality often encountered in multiparameter estimation problems is obtained. Using these solutions as guidelines, improved estimators for the scale parameters as well as the natural parameters of independent gamma distributions are obtained for a large class of weighted quadratic losses. The improved estimators have an empirical Bayes interpretation. They also permit an exact analytical representation of the risk improvement. For the ordinary squared-error loss, a larger class of improved estimates is obtained which may allow for incorporation of prior information in choosing an alternative estimate. Numerical results are given which indicate the extent of risk improvement in certain situations.


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Anirban Das Gupta. "Simultaneous Estimation in the Multiparameter Gamma Distribution Under Weighted Quadratic Losses." Ann. Statist. 14 (1) 206 - 219, March, 1986.


Published: March, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0602.62011
MathSciNet: MR829563
Digital Object Identifier: 10.1214/aos/1176349850

Primary: 62C15
Secondary: 62F10, 62H99

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 1 • March, 1986
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