English

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 2\ell_{2}-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.

Keywords

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}
}
R2 v1 2026-06-21T20:26:20.478Z