Institute of Mathematical Statistics Lecture Notes - Monograph Series

Asymptotic Efficiency of Simple Decisions for the Compound Decision Problem

Eitan Greenshtein and Ya’acov Ritov

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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.

Chapter information

Source
Javier Rojo, ed., Optimality: The Third Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 266-275

Dates
First available in Project Euclid: 3 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1249305334

Digital Object Identifier
doi:10.1214/09-LNMS5716

Mathematical Reviews number (MathSciNet)
MR2681676

Zentralblatt MATH identifier
1271.62022

Subjects
Primary: 62C25: Compound decision problems
Secondary: 62C12: Empirical decision procedures; empirical Bayes procedures 62C07: Complete class results

Keywords
compound decision simple decision rules permutation invariant rules

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

Rojo, Javier. Asymptotic Efficiency of Simple Decisions for the Compound Decision Problem. Optimality, 266--275, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-LNMS5716. https://projecteuclid.org/euclid.lnms/1249305334


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