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September, 1958 Admissible and Minimax Integer-Valued Estimators of an Inter-Valued Parameter
D. S. Robson
Ann. Math. Statist. 29(3): 801-812 (September, 1958). DOI: 10.1214/aoms/1177706537


The decision problem considered here is that of deciding which element of a finite parametric family of probability distributions $p(x, \mu)$ represents the true distribution of the statistic $X$. It is assumed that $p(x, \mu)$ satisfies certain regularity conditions which essentially require that the parameter $\mu$ be integer-valued with known bounds and that $p(x, \mu_1)/p(x, \mu_0)$ be an increasing function of $x$ whenever $\mu_0 < \mu_1$. Complete classes are characterized for various loss functions $W(\mu, \alpha)$ which are convex functions of the decision $\alpha$ for each fixed value of $\mu$. Minimax procedures are considered for the case $W(\mu, \alpha) = |\alpha - \mu|^k$.


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D. S. Robson. "Admissible and Minimax Integer-Valued Estimators of an Inter-Valued Parameter." Ann. Math. Statist. 29 (3) 801 - 812, September, 1958.


Published: September, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0135.19501
MathSciNet: MR96339
Digital Object Identifier: 10.1214/aoms/1177706537

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 3 • September, 1958
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