%0 Journal Article
%T Marshall's lemma for convex density estimation
%A Lutz Duembgen
%A Kaspar Rufibach
%A Jon A. Wellner
%J Mathematics
%D 2006
%I arXiv
%R 10.1214/074921707000000292
%X Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies $\sqrt{n}$--consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on $[0,\infty)$.
%U http://arxiv.org/abs/math/0609277v2