Estimation of a convex discrete distribution
Methodology
2012-02-29 v1
Abstract
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 -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.
Cite
@article{arxiv.1202.6263,
title = {Estimation of a convex discrete distribution},
author = {Cécile Durot and François Koladjo and Sylvie Huet and Stéphane Robin},
journal= {arXiv preprint arXiv:1202.6263},
year = {2012}
}