On the strong consistency of approximated M-estimators

Djalil Chafai (1, 2) , Didier Concordet (1, 2)

1 LSP - Laboratoire de Statistique et Probabilités
2 UPTE - Physiopathologie et Toxicologie Expérimentales

The aim of this article is to provide a strong consistency Theorem for approximated M-estimators. It contains both Wald and Pfanzagl type results for maximum likelihood. The proof relies, in particular, on the existence of a sort of contraction of the parameter space which admits the true parameter as a fixed point. In a way, it can be seen as a simplification of ideas of Wang and Pfanzagl, generalised to approximated M-estimators. Proofs are short and elementary.

Mots clés: Estimators; Consistency; Maximum likelihood; Inverse Problems; Mixture models; Semiparametric models; Nonparametric models

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Djalil Chafai, Didier Concordet. On the strong consistency of approximated M-estimators. 2005. ⟨hal-00005835v1⟩