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arXiv · 2604.11489

Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets

Zhen Hong Yu·Yu Miao
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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.

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Zhen Hong Yu, Yu Miao. 2026-04-13. Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets. https://arxiv.org/abs/2604.11489

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