Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 49--66

CONSISTENT ESTIMATION OF THE ORDER OF MIXTURE MODELS

By

C. KERIBIN, Université Paris-Sud, Laboratoire de Mathématique, 91405 Orsay

SUMMARY. In this paper, we consider the estimation of the number of components for mixture models using a maximum penalized likelihood method. Leroux (1992) proved, under some assumptions, that the method leads to an estimator which, asymptotically, does not underestimate the number of components a.s.. We prove here the almost sure consistency of the maximum penalized likelihood estimator for an appropriate penalization sequence. The proof uses the locally conic parameterization developed by Dacunha-Castelle and Gassiat (1997). A numerical study of the choice of the penalization term is proposed, as well as a comparison with a moment method.

AMS (1991) subject classification. 62F05, 62H30, 62A10.

Key words and phrases. Model selection, maximum penalized likelihood, non identifiable models, mixtures.

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