Entropic representation and estimation of diversity indices

Zhiyi Zhang and Michael Grabchak

Journal of Nonparametric Statistics, 2016, vol. 28, issue 3, 563-575

Abstract: This paper serves a twofold purpose. First, a unified perspective on diversity indices is introduced based on an entropic basis. It is shown that the class of all linear combinations of the entropic basis, referred to as the class of linear diversity indices, covers a wide range of diversity indices used in the literature. Second, a class of estimators for linear diversity indices is proposed and it is shown that these estimators have rapidly decaying biases and asymptotic normality.

Date: 2016
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DOI: 10.1080/10485252.2016.1190357

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