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arXiv · 1404.4830

Nonparametric species richness estimation under convexity constraint

Cécile Durot·Sylvie Huet·François Koladjo·Stéphane Robin
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Abstract

We consider the estimation of the total number $N$ of species based on the abundances of species that have been observed. We adopt a non parametric approach where the true abundance distribution $p$ is only supposed to be convex. From this assumption, we propose a definition for convex abundance distributions. We use a least-squares estimate of the truncated version of $p$ under the convexity constraint. We deduce two estimators of the total number of species, the asymptotic distribution of which are derived. We propose three different procedures, including a bootstrap one, to obtain a confidence interval for $N$. The performances of the estimators are assessed in a simulation study and compared with competitors. The proposed method is illustrated on several examples.

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Cécile Durot, Sylvie Huet, François Koladjo, Stéphane Robin. 2014-04-18. Nonparametric species richness estimation under convexity constraint. https://arxiv.org/abs/1404.4830

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