Likelihood ratio inequalities with applications to various mixtures
Estimation semi-paramétrique d'un modèle autorégressif stationnaire multiindice non nécessairement causal
The likelihood ratio test for the number of components in a mixture with Markov regime
The likelihood ratio test for the number of components in a mixture with Markov regime
We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime. We prove that the LRT statistic converges to infinity in probability as the number of observations tends to infinity. This is a consequence of a convergence result of the LRT statistic for a subproblem where the parameters are restricted to a subset of the whole parameter set.
Testing in locally conic models, and application to mixture models
In this paper, we address the problem of testing hypotheses using maximum likelihood statistics in non identifiable models. We derive the asymptotic distribution under very general assumptions. The key idea is a local reparameterization, depending on the underlying distribution, which is called locally conic. This method enlights how the general model induces the structure of the limiting distribution in terms of dimensionality of some derivative space. We present various applications of...
The likelihood ratio test for general mixture models with or without structural parameter
This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations...
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