SMOOTH MIN-DIVERGENCE INFERENCE IN SEMI PARAMETRIC MODELS

Michel Broniatowski (1) , Justin Steward Moutsouka

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

This paper considers inference in some semi parametric models through some speci…c class of statistical procedure, which have proved to be of valuable interest in parametric estimation, namely the power divergence family de…ned by Basu Hodjt, Harris and Jones (1998). At a …rst glance their divergence is not …tted to semiparametric inference. However extending the parametric setting to a smoothed semiparametric one, it is possible to make inference both on T and on the density of P T in semiparamet-ric models de…ned by moment conditions indexed by some parameter , where the data are generated under some unknown T : This question is of interest; indeed usually the estimation of the density of P T with respect to a dominating measure (here the Lebesgue measure) is an open chalenge in the realm of semi parametric models. This is the focus of the present paper.

Mots clés: and phrases :Semi parametric models; Inference; Minimum di- vergence inference

Domaines: Statistiques [math.ST]

Michel Broniatowski, Justin Steward Moutsouka. SMOOTH MIN-DIVERGENCE INFERENCE IN SEMI PARAMETRIC MODELS. 2020. ⟨hal-02586204⟩