English

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 n\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,)[0,\infty).

Keywords

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)