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Entropic representation and estimation of diversity indices

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  • Zhiyi Zhang
  • Michael Grabchak

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.

Suggested Citation

  • Zhiyi Zhang & Michael Grabchak, 2016. "Entropic representation and estimation of diversity indices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 563-575, September.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:563-575
    DOI: 10.1080/10485252.2016.1190357
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    Cited by:

    1. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Zhang, Jialin & Shi, Jingyi, 2024. "Nonparametric clustering of discrete probability distributions with generalized Shannon’s entropy and heatmap," Statistics & Probability Letters, Elsevier, vol. 208(C).

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