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June, 1989 Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression
Robert E. Kelly
Ann. Statist. 17(2): 937-940 (June, 1989). DOI: 10.1214/aos/1176347153


Consider the problem of estimating the ordered means $\mu_1 \leq \mu_2 \leq \cdots \leq \mu_k$ of independent normal random variables, $Y_1, Y_2, \cdots, Y_k$. It is shown that the absolute error of each component $\hat{\mu}_i$ of the isotonic regression estimator is stochastically smaller than that of the usual estimator $Y_i$. Thus $\hat{\mu}_i$ is superior to $Y_i$ under any nonconstant loss which is a nondecreasing function of absolute error.


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Robert E. Kelly. "Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression." Ann. Statist. 17 (2) 937 - 940, June, 1989.


Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0673.62021
MathSciNet: MR994278
Digital Object Identifier: 10.1214/aos/1176347153

Primary: 62F10
Secondary: 60E15 , 62C99 , 62E99

Keywords: isotonic regression , loss function , maximum likelihood , order restriction , stochastic ordering

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 2 • June, 1989
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