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VOL. 55 | 2007 Marshall’s lemma for convex density estimation
Lutz Dümbgen, Kaspar Rufibach, Jon A. Wellner

Editor(s) Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, 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 $[0,\infty)$.

Information

Published: 1 January 2007
First available in Project Euclid: 4 December 2007

zbMATH: 1176.62029

Digital Object Identifier: 10.1214/074921707000000292

Subjects:
Primary: 62G05, 62G20, 62G20

Rights: Copyright © 2007, Institute of Mathematical Statistics

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