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VOL. 57 | 2009 Asymptotic Efficiency of Simple Decisions for the Compound Decision Problem

Abstract

We consider the compound decision problem of estimating a vector of n parameters, known up to a permutation, corresponding to n independent observations, and discuss the difference between two symmetric classes of estimators. The first and larger class is restricted to the set of all permutation invariant estimators. The second class is restricted further to simple symmetric procedures. That is, estimators such that each parameter is estimated by a function of the corresponding observation alone. We show that under mild conditions, the minimal total squared error risks over these two classes are asymptotically equivalent up to essentially O(1) difference.

Information

Published: 1 January 2009
First available in Project Euclid: 3 August 2009

zbMATH: 1271.62022
MathSciNet: MR2681676

Digital Object Identifier: 10.1214/09-LNMS5716

Subjects:
Primary: 62C25
Secondary: 62C07, 62C12

Rights: Copyright © 2009, Institute of Mathematical Statistics

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