Institute of Mathematical Statistics Lecture Notes - Monograph Series
- Lecture Notes--Monograph Series
- Volume 55, 2007, 101-107
Marshall’s lemma for convex density estimation
Lutz Dümbgen, Kaspar Rufibach, and Jon A. Wellner
Abstract
Marshall's lemma is an analytical result which implies $\sqrt{n}$--consistency of the distribution function corresponding to the Grenander estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on $[0,\infty)$.
Chapter information
Source
Dates
First available in Project Euclid: 4 December 2007
Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196797070
Digital Object Identifier
doi:10.1214/074921707000000292
Zentralblatt MATH identifier
1176.62029
Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties 62G20: Asymptotic properties
Keywords
empirical distribution function inequality least squares maximum likelihood shape constraint supremum norm
Rights
Copyright © 2007, Institute of Mathematical Statistics
Citation
Dümbgen, Lutz; Rufibach, Kaspar; Wellner, Jon A. Marshall’s lemma for convex density estimation. Asymptotics: Particles, Processes and Inverse Problems, 101--107, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000292. https://projecteuclid.org/euclid.lnms/1196797070
