Marshall's lemma for convex density estimation
Statistics Theory
2023-04-17 v2 Statistics Theory
Abstract
Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies --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 .
Cite
@article{arxiv.math/0609277,
title = {Marshall's lemma for convex density estimation},
author = {Lutz Duembgen and Kaspar Rufibach and Jon A. Wellner},
journal= {arXiv preprint arXiv:math/0609277},
year = {2023}
}
Comments
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)