Institute of Mathematical Statistics Lecture Notes - Monograph Series
- 2009, 266-275
Asymptotic Efficiency of Simple Decisions for the Compound Decision Problem
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.
First available in Project Euclid: 3 August 2009
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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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