We consider modified empirical Bayes problems in which the prior distribution of $\Theta$ at stage $n + 1$ is $G^{(n+1)}(\theta)$. The Bayes optimality criterion is now given by the sequence of functionals $R(G^{(n+1)}$. The observations $X_1, \cdots, X_n$ are no longer i.i.d so decision procedures are constructed based on modified empirical density estimates for $f_G^{(n+1)}(x)$. Asymptotic optimality together with asymptotic convergence rates is established for two action and estimation problems when the observations are drawn from a member of the one-parameter exponential family.
Publié le : 1984-09-14
Classification:
Empirical Bayes,
modified optimality,
criterion,
rates of convergence,
62C10,
62C12
@article{1176346722,
author = {Mara, M. K. and Deely, J. J.},
title = {Empirical Bayes with a Changing Prior},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 1071-1078},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346722}
}
Mara, M. K.; Deely, J. J. Empirical Bayes with a Changing Prior. Ann. Statist., Tome 12 (1984) no. 1, pp. 1071-1078. http://gdmltest.u-ga.fr/item/1176346722/