The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density
estimates are useful. Asymptotic minimax-type lower bounds are obtained for the unconditional regret, and empirical Bayes rules based on kernel density estimates are shown to possess a certain optimal asymptotic minimax
property.
Publié le : 1996-02-14
Classification:
Empirical Bayes,
monotone tests,
asymptotically optimal,
rates of convergence,
62C12,
62F03,
62C20
@article{1033066207,
author = {Karunamuni, Rohana J.},
title = {Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 212-231},
language = {en},
url = {http://dml.mathdoc.fr/item/1033066207}
}
Karunamuni, Rohana J. Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family. Ann. Statist., Tome 24 (1996) no. 6, pp. 212-231. http://gdmltest.u-ga.fr/item/1033066207/