2012/02/28 by Cécile Durot, Durot, Cécile, François Koladjo +5
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME
paper · pdf · doi:10.48550/arxiv.1202.6263
arxiv created 2012/02/28 · arxiv updated 2012/02/29
Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete distribution under the constraint of convexity. We show that this estimator exists and is unique, and that it always outperforms the classical empirical estimator in terms of the ℓ2-distance. We provide an algorithm for its computation, based on the support reduction algorithm. We compare its performance to those of the empirical estimator, on the basis of a simulation study.