The Annals of Statistics

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

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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.

Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1137-1147.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345979

Digital Object Identifier
doi:10.1214/aos/1176345979

Mathematical Reviews number (MathSciNet)
MR673649

Zentralblatt MATH identifier
0526.62005

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section 39A10: Difference equations, additive

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

Citation

Hwang, Jiunn Tzon. 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 (1982), no. 4, 1137--1147. doi:10.1214/aos/1176345979. https://projecteuclid.org/euclid.aos/1176345979


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