New results on mixture and exponential models by Orlicz spaces

TL;DR

This paper introduces new theoretical results on nonparametric exponential and mixture models, utilizing Orlicz spaces to provide characterizations and address open questions in the field.

Contribution

It offers novel characterizations of maximal exponential models through Orlicz spaces and exponential arcs, advancing the theoretical understanding of these models.

Findings

Characterizations of maximal exponential models using Orlicz spaces

Examples and counterexamples supporting the theoretical results

Answers to open questions in the literature

Abstract

New results and improvements in the study of nonparametric exponential and mixture models are proposed. In particular, different equivalent characterizations of maximal exponential models, in terms of open exponential arcs and Orlicz spaces, are given. Our theoretical results are supported by several examples and counterexamples and provide an answer to some open questions in the literature.