A class of non-parametric deformed exponential statistical models

TL;DR

This paper explores a broad class of non-parametric deformed exponential models with specific growth properties, generalizing previous models and analyzing their mathematical structure and divergence measures.

Contribution

It introduces a generalized class of deformed exponential models with detailed analysis of their convexity, divergence, and geometric properties, extending prior work by Newton.

Findings

The deformed exponential has linear growth at infinity.

The class generalizes Newton's models.

Properties of divergence and escort densities are characterized.

Abstract

We study the class on non-parametric deformed statistical models where the deformed exponential has linear growth at infinity and is sub-exponential at zero. This class generalizes the class introduced by N.J.~Newton. We discuss the convexity and regularity of the normalization operator, the form of the deformed statistical divergences and their convex duality, the properties of the escort densities, and the affine manifold structure of the statistical bundle.