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March, 1991 Simultaneous Estimation in Discrete Multivariate Exponential Families
Jine-Phone Chou
Ann. Statist. 19(1): 314-328 (March, 1991). DOI: 10.1214/aos/1176347984


Let $X$ have a discrete density of the form $f(x) = t(x)\xi(\theta)\theta^{x_1}_1 \cdots \theta^{x_p}_p$, where $t(x)$ is nonzero on some infinite subset of $Z^p$. Consider simultaneous estimation of the $\theta_i$ under the loss $\mathscr{L}_m(\theta, \delta) = \sum^p_{i = 1} \theta^{-m}_i(\theta_i - \delta_i)^2, m \geq 0$. For integers $m \geq 1$, estimators are found which improve on the maximum likelihood estimator or uniformly minimum variance unbiased estimator. The improved estimators are distinguished by the property that they do not depend on $m$ for "large values" of the observed vector. On the other hand, we prove admissibility of a class of estimators, including the MLE and UMVUE, for some discrete densities of the indicated form under squared error loss $(m = 0)$.


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Jine-Phone Chou. "Simultaneous Estimation in Discrete Multivariate Exponential Families." Ann. Statist. 19 (1) 314 - 328, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0728.62033
MathSciNet: MR1091853
Digital Object Identifier: 10.1214/aos/1176347984

Primary: 62C15
Secondary: 62F10 , 62H99

Keywords: Admissibility , Discrete multivariate exponential families , maximum likelihood estimators , negative multinomial distribution , quota fulfillment , uniformly minimum variance unbiased estimators

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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