Marshall's lemma for convex density estimation

Abstract

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 $[0,\infty )$.

Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (3)

• Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
• A Kiefer--Wolfowitz theorem for convex densities
• On Convex Least Squares Estimation when the Truth is Linear