Sub-exponentiality in Statistical Exponential Models

Improvements 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 thesemodels. The explicit constantswe obtainwhen changing the lawof Orlicz spaces centered at connected densities allow us to derive uniform bounds with respect to a reference density.