2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139456The 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.Accepted for publication in Journal of Statistical Planning and InferenceStatistics TheoryProbability62G05; 62F12; 34K29; 60F99text