Asymptotic and finite-sample distributions of one- and two-sample empirical relative entropy

Matthieu Garcin and Louis Perot

Papers from arXiv.org

Abstract: In the perspective of building statistical tests of divergence between two probability distributions, we study the distribution of empirical relative entropy and derive several types of approximations: concentration inequalities for finite samples, asymptotic distributions, and Berry-Esseen bounds in a pre-asymptotic regime. For the latter, we introduce a new approach to obtain Berry-Esseen inequalities for nonlinear functions of sum statistics under some convexity assumptions. Our theoretical contributions cover both one- and two-sample empirical relative entropies.

Date: 2025-12, Revised 2026-07
New Economics Papers: this item is included in nep-ecm and nep-ets
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