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


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.


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


Published: august 1999
First available in Project Euclid: 19 February 2007

zbMATH: 0929.62015
MathSciNet: MR1704563

Keywords: asymptotic distribution , contamination , homogeneity , likelihood ratio , mixture distribution

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability


Vol.5 • No. 4 • august 1999
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