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arXiv · 2508.12382

Moderate deviation principle for plug-in estimators of diversity indices on countable alphabets

Zhenhong Yu·Yu Miao
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Abstract

In the present paper, we consider the moderate deviation principle for the plug-in estimators of a large class of diversity indices on countable alphabets, where the distribution may change with the sample size. Our results cover some of the most commonly used indices, including Tsallis entropy, Re\'{n}yi entropy and Hill diversity number.

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Zhenhong Yu, Yu Miao. 2025-08-17. Moderate deviation principle for plug-in estimators of diversity indices on countable alphabets. https://arxiv.org/abs/2508.12382

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