Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets
Probability
2026-04-14 v1
Abstract
In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the plug-in estimator of a wide class of indices, including Simpson's index and Re\'{n}yi's entropy. For the practically crucial case of Shannon entropy, we provide explicit Berry-Esseen bounds for the standard plug-in estimator, as well as for two widely used bias-corrected variants, the Miller-Madow and the jackknife estimators.
Cite
@article{arxiv.2604.11489,
title = {Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets},
author = {Zhen Hong Yu and Yu Miao},
journal= {arXiv preprint arXiv:2604.11489},
year = {2026}
}