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Nonparametric species richness estimation under convexity constraint
Author(s) -
Durot Cécile,
Huet Sylvie,
Koladjo François,
Robin Stéphane
Publication year - 2015
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2352
Subject(s) - estimator , nonparametric statistics , mathematics , convexity , constraint (computer aided design) , abundance (ecology) , asymptotic distribution , statistics , confidence interval , standard error , distribution (mathematics) , mathematical analysis , ecology , biology , economics , geometry , financial economics
We consider the estimation of the number N of present species in a given area at a given time, based on the abundances of species that have been observed. We adopt a nonparametric approach where the true abundance distribution p is only supposed to be convex. A definition for convex abundance distributions is proposed. A least‐squares estimate of the truncated version of p under the convexity constraint is used. Two estimators of N are deduced, the asymptotic distribution of which are derived. We propose three different procedures, including a bootstrap one, to obtain a confidence interval for N and a standard error for its estimator. The performances of the estimators are assessed in a simulation study and compared with competitors. The proposed method is illustrated on several examples. Copyright © 2015 John Wiley & Sons, Ltd.