Asymptotic normality for plug-in estimators of diversity indices on countable alphabets |
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Authors: | Michael Grabchak Zhiyi Zhang |
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Institution: | The University of North Carolina at Charlotte, Charlotte, NC, USA |
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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. |
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Keywords: | Diversity indices asymptotic normality entropy estimation |
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