Likelihood ratio tests in contamination models. (English) Zbl 0929.62015

Lemdani, Mohamed; Pons, Odile

Bernoulli 5, No. 4, 705-719 (1999).

Summary: We study the asymptotic distribution of the likelihood ratio statistic to test whether the contamination of a known density \(f_0\) by another density of the same parametric family reduces to \(f_0\). 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.

MSC:

62F05	Asymptotic properties of parametric tests
62E20	Asymptotic distribution theory in statistics

Keywords:

homogeneity; likelihood ratio; mixture distribution; contamination