Nonparametric species richness estimation under convexity constrain
Résumé
We consider the estimation of the total number N of species 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. From this assumption, we propose a de finition 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 di erent procedures, including a bootstrap one, to obtain a con dence interval for N. The performances of the estimators are assessed in a simulation study and compared with competitor. The proposed method is illustrated on several examples.