Sub-exponentiality in Statistical Exponential Models

Abstract

AbstractImprovements in the study of nonparametric maximal exponential models built on Orlicz spaces are proposed. By exploiting the notion of sub-exponential random variable, we give theoretical results which provide a clearer insight into the structure of these models. The explicit constants we obtain when changing the law of Orlicz spaces centered at connected densities allow us to derive uniform bounds with respect to a reference density.