Bernoulli

  • Bernoulli
  • Volume 5, Number 4 (1999), 705-719.

Likelihood ratio tests in contamination models

Mohamed Lemdani and Odile Pons

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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.

Article information

Source
Bernoulli, Volume 5, Number 4 (1999), 705-719.

Dates
First available in Project Euclid: 19 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171899325

Mathematical Reviews number (MathSciNet)
MR1704563

Zentralblatt MATH identifier
0929.62015

Keywords
asymptotic distribution contamination homogeneity likelihood ratio mixture distribution

Citation

Lemdani, Mohamed; Pons, Odile. Likelihood ratio tests in contamination models. Bernoulli 5 (1999), no. 4, 705--719. https://projecteuclid.org/euclid.bj/1171899325


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