THE LIKELIHOOD RATIO TEST FOR GENERAL MIXTURE MODELS WITH OR WITHOUT STRUCTURAL PARAMETER

被引：19

作者：

Azais, Jean-Marc ^{[1
]}

Gassiat, Elisabeth ^{[2
]}

Mercadier, Cecile ^{[3
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, UMR 5219, F-31062 Toulouse 9, France

[2] Univ Paris 11, CNRS, UMR 8628, Equipe Probabilites Stat & Modelisat, F-91405 Orsay, France

[3] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

ESAIM-PROBABILITY AND STATISTICS | 2009年 / 13卷

关键词：

Likelihood ratio test; mixture models; number of components; local power; contiguity; ASYMPTOTIC-DISTRIBUTION; HOMOGENEITY; COMPONENTS; NUMBER; ORDER; POWER;

D O I：

10.1051/ps:2008010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 in a finite mixture with or without structural parameter.

引用

页码：301 / 327

页数：27

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