Asymptotic normality for plug-in estimators of diversity indices on countable alphabets

Michael Grabchak and Zhiyi Zhang

Journal of Nonparametric Statistics, 2018, vol. 30, issue 3, 774-795

Abstract: The plug-in estimator is one of the most popular approaches to the estimation of diversity indices. In this paper, we study its asymptotic distribution for a large class of diversity indices on countable alphabets. In particular, we give conditions for the plug-in estimator to be asymptotically normal, and in the case of uniform distributions, where asymptotic normality fails, we give conditions for the asymptotic distribution to be chi-squared. Our results cover some of the most commonly used indices, including Simpson's index, Reńyi's entropy and Shannon's entropy.

Date: 2018
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DOI: 10.1080/10485252.2018.1482294

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