Least-squares estimation of a convex discrete distribution

Cécile Durot (1) , Sylvie Huet , Francois Koladjo , Stephane S. Robin

1 MODAL'X - Modélisation aléatoire de Paris X

The least squares estimator of a discrete distribution under the constraint of convexity is introduced. Its existence and uniqueness are shown and consistency and rate of convergence are established. Moreover it is shown that it always outperforms the classical empirical estimator in terms of the Eu-clidean distance. Results are given both in the well-and the mis-specified cases. The performance of the estimator is checked throughout a simulation study. An algorithm, based on the support reduction algorithm, is provided. Application to the estimation of species abundance distribution is discussed.

Mots clés: convex discrete distribution; nonparametric estimation; least squares; support reduction algorithm; abundance distribution

Domaines: Théorie [stat.TH]; Statistiques [stat]

Cécile Durot, Sylvie Huet, Francois Koladjo, Stephane S. Robin. Least-squares estimation of a convex discrete distribution. Computational Statistics and Data Analysis, 2013. ⟨hal-01712994⟩