publication . Preprint . Article . 2016

Entropic Representation and Estimation of Diversity Indices

Zhiyi Zhang; Michael Grabchak;
Open Access English
  • Published: 08 Jun 2016
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.
Subjects
free text keywords: Mathematics - Statistics Theory, Statistics, Probability and Uncertainty, Statistics and Probability, Diversity index, Linear combination, Econometrics, Estimator, Statistics, Mathematics, Asymptotic distribution
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