In this paper we are interested in empirical likelihood (EL) as a method of estimation, and we address the following two problems: (1) selecting among various empirical discrepancies in an EL framework and (2) demonstrating that EL has a well-defined probabilistic interpretation that would justify its use in a Bayesian context. Using the large deviations approach, a Bayesian law of large numbers is developed that implies that EL and the Bayesian maximum a posteriori probability (MAP) estimators are consistent under misspecification and that EL can be viewed as an asymptotic form of MAP. Estimators based on other empirical discrepancies are, in general, inconsistent under misspecification.
Publié le : 2009-10-15
Classification:
Maximum nonparametric likelihood,
estimating equations,
Bayesian nonparametric consistency,
Bayesian large deviations,
L-divergence,
Pólya sampling,
right censoring,
Kaplan–Meier estimator,
62G05,
62C10,
60F10
@article{1247663761,
author = {Grend\'ar, Marian and Judge, George},
title = {Asymptotic equivalence of empirical likelihood and Bayesian MAP},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 2445-2457},
language = {en},
url = {http://dml.mathdoc.fr/item/1247663761}
}
Grendár, Marian; Judge, George. Asymptotic equivalence of empirical likelihood and Bayesian MAP. Ann. Statist., Tome 37 (2009) no. 1, pp. 2445-2457. http://gdmltest.u-ga.fr/item/1247663761/