Using the variational properties of epi-convergence together with suitable results on the measurability of multifunctions and integrands, we prove a strong law of large numbers for sequences of integrands from which we
deduce a general theorem of almost sure convergence (strong consistency) for the maximum likelihood estimator.
Publié le : 1996-06-14
Classification:
Maximum likelihoood estimator,
strong consistency,
measurable multifunctions,
normal integrands,
set convergence,
epi-convergence,
28B20,
49K45,
54D35,
62F12,
62H12,
62L20
@article{1032526970,
author = {Hess, Christian},
title = {Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1298-1315},
language = {en},
url = {http://dml.mathdoc.fr/item/1032526970}
}
Hess, Christian. Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. Ann. Statist., Tome 24 (1996) no. 6, pp. 1298-1315. http://gdmltest.u-ga.fr/item/1032526970/