APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RENYI DIVERGENCES.

ABSTRACT: In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Q_n → Q in the Wasserstein metric, then the projected densities converge in weighted L₁ metrics and uniformly on closed subsets of the continuity set of the limit. Moreover, directional derivatives of the projected densities also enjoy local uniform convergence. T

SUBMITTER: Han Q 

PROVIDER: S-EPMC5619680 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature