An empirical Bayes test for testing $\vartheta \leq \vartheta_0$ against $\vartheta > \vartheta_0$ for the uniform distribution on $\lbrack 0, \vartheta)$ is discussed. The relation is shown with the estimation of a decreasing density on $\lbrack 0, \infty)$ and a monotone empirical Bayes test is derived based on the least-concave majorant of the empirical distribution function. The asymptotic distribution of the Bayes risk is obtained and some Monte Carlo results are given.
Publié le : 1987-06-14
Classification:
Empirical Bayes,
monotone test,
uniform distribution,
decreasing density,
maximum likelihood estimator,
concave majorant,
62C12,
62F12
@article{1176350381,
author = {van Houwelingen, J. C.},
title = {Monotone Empirical Bayes Test for Uniform Distributions Using the Maximum Likelihood Estimator of a Decreasing Density},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 875-879},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350381}
}
van Houwelingen, J. C. Monotone Empirical Bayes Test for Uniform Distributions Using the Maximum Likelihood Estimator of a Decreasing Density. Ann. Statist., Tome 15 (1987) no. 1, pp. 875-879. http://gdmltest.u-ga.fr/item/1176350381/