On nonparametric maximum likelihood for a class of stochastic inverse problems

Djalil Chafai (1, 2) , Jean-Michel Loubes (3)

1 LSP - Laboratoire de Statistique et Probabilités
2 UPTE - Physiopathologie et Toxicologie Expérimentales
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We establish the consistency of a nonparametric maximum likelihood estimator for a class of stochastic inverse problems. We proceed by embedding the framework into the general settings of early results of Pfanzagl related to mixtures.

Mots clés: Maximum Likelihood; EM Algorithm; Inverse Problems; Nonlinear Models; Repeated Measurments Data; Longitudinal Data; Longitudinal Data.; Mixtures of Probability Measures

Domaines: Statistiques [math.ST]

Djalil Chafai, Jean-Michel Loubes. On nonparametric maximum likelihood for a class of stochastic inverse problems. Statistics and Probability Letters, 2006, 76 (12), pp.1225-1237. ⟨10.1016/j.spl.2005.12.019⟩. ⟨hal-00003341⟩