Open Access
Translator Disclaimer
December, 1982 Semi Tail Upper Bounds on the Class of Admissible Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Distributions
Jiunn Tzon Hwang
Ann. Statist. 10(4): 1137-1147 (December, 1982). DOI: 10.1214/aos/1176345979

Abstract

Admissibility problems involving simultaneous estimation in discrete exponential families are studied by solving difference inequalities. It is shown that if an estimator is admissible under the loss function $L_m(\mathbf{\theta, a)} = \sum^p_{i = 1} \theta^{m_i}_i (\theta_i - a_i)^2$, then in the tail (i.e., for large values of the observations), this estimator has to be less than certain bounds. Specific bounds, called Semi Tail Upper Bounds (STUB), are given here. These STUBs are not only of theoretical interest, but also are sharp enough that they establish many new results. Two of the most interesting ones are: (i) the establishment of Brown's conjecture concerning inadmissibility of some of the estimators proposed by Clevenson and Zidek (1975), and (ii) the establishment of inadmissibility of Hudson's (1978) estimator which improves upon the uniformly minimum variance unbiased estimator in Negative Binomial families.

Citation

Download Citation

Jiunn Tzon Hwang. "Semi Tail Upper Bounds on the Class of Admissible Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Distributions." Ann. Statist. 10 (4) 1137 - 1147, December, 1982. https://doi.org/10.1214/aos/1176345979

Information

Published: December, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0526.62005
MathSciNet: MR673649
Digital Object Identifier: 10.1214/aos/1176345979

Subjects:
Primary: 62C15
Secondary: 39A10 , 62F10 , 62H99

Keywords: Admissibility , difference inequality , discrete exponential family , loss function , negative binomial distribution , Poisson distribution

Rights: Copyright © 1982 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.10 • No. 4 • December, 1982
Back to Top