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Asymptotic theory of the log-likelihood ratio test for mixtures with two components. (Théorie asymptotique du test du rapport des vraisemblances d’un mélange à deux composants.) (French) Zbl 0897.62020
Summary: We show how it is possible to remove the separation condition given by J. K. Gosh and P. K. Sen [in L. Le Cam and A. Olshen (eds.), Proc. Berkeley Conf. Honor J. Neyman and J. Kiefer, 789-806 (1985)], in the problem of testing homogeneity versus a mixture with two components via the likelihood ratio test. The asymptotic expression of the test is given with the usual parameterization. Some applications are considered.
MSC:
62F05 Asymptotic properties of parametric tests
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