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

TL;DR

This paper establishes the moderate deviation principle for plug-in estimators of various diversity indices on countable alphabets, accounting for changing distributions with sample size, and covering indices like Tsallis, Rényi, and Hill diversity.

Contribution

It introduces the moderate deviation principle for a broad class of diversity estimators on countable alphabets with dynamic distributions, extending existing theoretical frameworks.

Findings

Moderate deviation principles are proven for multiple diversity indices.

Results apply to indices like Tsallis, Rényi, and Hill diversity.

The study accounts for distribution changes with sample size.

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.