Stability of Cramer's Characterization of Normal Laws in Information Distances

TL;DR

This paper establishes stability estimates for the characterization of normal distributions using information distances, enhancing understanding of how close distributions are to normality under Cramer's theorem.

Contribution

It provides new stability bounds for normal law characterization in terms of relative entropy and Fisher information, extending previous results.

Findings

Derived stability estimates in relative entropy and Fisher information.

Quantified how regularized distributions approximate normal laws.

Improved understanding of distribution closeness in information-theoretic terms.

Abstract

Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer's theorem with respect to relative entropy and Fisher information distance.