Abstract
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.
Citation
Mohamed Lemdani. Odile Pons. "Likelihood ratio tests in contamination models." Bernoulli 5 (4) 705 - 719, august 1999.
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