On the strong consistency of asymptotic 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 simplify Pfanzagl's proof of consistency for asymptotic maximum likelihood estimators, and to extend it to more general asymptotic M-estimators. The method relies on the existence of a sort of contraction of the parameter space which admits the true parameter as a fixed point. The 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 asymptotic M-estimators. Journal of Statistical Planning and Inference, 2007, 137 (9), pp.2774-2783. ⟨10.1016/j.jspi.2006.09.027⟩. ⟨hal-00005835v2⟩