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March, 1979 Admissible and Minimax Estimation for the Multinomial Distribution and for K Independent Binomial Distributions
Ingram Olkin, Milton Sobel
Ann. Statist. 7(2): 284-290 (March, 1979). DOI: 10.1214/aos/1176344613

Abstract

Admissible and minimax estimation is discussed for estimating the parameters in the (a) multinomial distribution and in (b) $k$ independent binomial distributions. In (a) the loss function is $\sum^n_0\lbrack\delta_i(x) - \theta_i\rbrack^2/\theta_i$, where $\theta_0, \cdots, \theta_k(\sum\theta_i = 1)$ are the parameters in the multinomial distribution, and the estimators are restricted to $\sum^k_0\delta_i(x) = 1$. In (b) the loss functions considered are the weighted sum of quadratic losses. The method of proof is based on a multivariate analog of the Cramer-Rao inequality, and uses the divergence theorem in a novel way.

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Ingram Olkin. Milton Sobel. "Admissible and Minimax Estimation for the Multinomial Distribution and for K Independent Binomial Distributions." Ann. Statist. 7 (2) 284 - 290, March, 1979. https://doi.org/10.1214/aos/1176344613

Information

Published: March, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0407.62005
MathSciNet: MR520240
Digital Object Identifier: 10.1214/aos/1176344613

Subjects:
Primary: 62C15
Secondary: 62H15

Keywords: admissible estimators , divergence theorem , independent binomial distributions , minimax estimators , multinomial distribution , multivariate Cramer-Rao inequality

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 2 • March, 1979
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