Institute of Mathematical Statistics Lecture Notes - Monograph Series

Marshall’s lemma for convex density estimation

Lutz Dümbgen, Kaspar Rufibach, and Jon A. Wellner

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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

Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner, eds., Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 101-107

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties 62G20: Asymptotic properties

empirical distribution function inequality least squares maximum likelihood shape constraint supremum norm

Copyright © 2007, Institute of Mathematical Statistics


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.

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