We study the asymptotic distribution of the likelihood ratio statistic to test whether the contamination of a known density f0 by another density of the same parametric family reduces to f0. The classical asymptotic theory for the likelihood ratio statistic fails, and we propose a general reparametrization which ensures regularity properties. Under the null hypothesis, the likelihood ratio statistic converges to the supremum of a squared truncated Gaussian process. The result is extended to the case of the contamination of a mixture of p known densities by q other densities of the same family.
Publié le : 1999-08-14
Classification:
asymptotic distribution,
contamination,
homogeneity,
likelihood ratio,
mixture distribution
@article{1171899325,
author = {Lemdani, Mohamed and Pons, Odile},
title = {Likelihood ratio tests in contamination models},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 705-719},
language = {en},
url = {http://dml.mathdoc.fr/item/1171899325}
}
Lemdani, Mohamed; Pons, Odile. Likelihood ratio tests in contamination models. Bernoulli, Tome 5 (1999) no. 6, pp. 705-719. http://gdmltest.u-ga.fr/item/1171899325/