On the strong consistency of approximated M-estimators
Résumé
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.