zbMATH — the first resource for mathematics

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.
62F05 Asymptotic properties of parametric tests