The Annals of Statistics

Simultaneous Estimation in the Multiparameter Gamma Distribution Under Weighted Quadratic Losses

Anirban Das Gupta

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Abstract

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.

Article information

Source
Ann. Statist., Volume 14, Number 1 (1986), 206-219.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349850

Digital Object Identifier
doi:10.1214/aos/1176349850

Mathematical Reviews number (MathSciNet)
MR829563

Zentralblatt MATH identifier
0602.62011

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

Keywords
Loss functions inadmissibility gamma scale parameters empirical Bayes linear estimates risk improvement

Citation

Gupta, Anirban Das. Simultaneous Estimation in the Multiparameter Gamma Distribution Under Weighted Quadratic Losses. Ann. Statist. 14 (1986), no. 1, 206--219. doi:10.1214/aos/1176349850. https://projecteuclid.org/euclid.aos/1176349850


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