Inference in phi-families of distributions

Bruno Pelletier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to the study of the parametric family of multivari- ate distributions obtained by minimizing a convex functional under linear constraints. Under certain assumptions on the convex functional, it is es- tablished that this family admits an affine parametrization, and parametric estimation from an i.i.d. random sample is studied. It is also shown that the members of this family are the limit distributions arising in inference based on empirical likelihood. As a consequence, given a probability measure μ0 and an i.i.d. random sample drawn from μ0, nonparametric confidence do- mains on the generalized moments of μ0 are obtained.

Keywords: generalized moment; Parametric statistics; Maximum entropy; φ-divergence; empirical likelihood; generalized moment.

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Bruno Pelletier. Inference in phi-families of distributions. Statistics A Journal of Theoretical and Applied Statistics, 2011, 45 (3), pp.223-236. ⟨hal-00460631⟩