On Optimal Solutions to Compound Statistical Decision Problems
Statistics Theory
2019-12-02 v2 Statistics Theory
Abstract
In a compound decision problem, consisting of statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule satisfies a natural symmetry property, entailing that for any permutation . We derive the greatest lower bound on the risk of any such decision rule. The classical problem of estimating the mean of a homoscedastic normal vector is used to demonstrate the theory, but important extensions are presented as well in the context of Robbins's original ideas.
Cite
@article{arxiv.1911.11422,
title = {On Optimal Solutions to Compound Statistical Decision Problems},
author = {Asaf Weinstein},
journal= {arXiv preprint arXiv:1911.11422},
year = {2019}
}
Comments
The main result is, apparently, already known. See, e.g., Berger (1985, Ch. 6), Greenshtein, E. & Ritov (2009)