Marshall's Lemma for Convex Density Estimation

Dümbgen, Lutz; Rufibach, Kaspar; Wellner, Jon (2007). Marshall's Lemma for Convex Density Estimation. In: Cator, Eric A.; Jongbloed, Geurt; Kraaikamp, Cor; Lopuhaä, Hendrik P.; Wellner, Jon A. (eds.) Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom. Lecture Notes - Monograph Series: Vol. 55 (pp. 101-107). Beachwood, Ohio, USA: Institute of Mathematical Statistics

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Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

Item Type:

Book Section (Book Chapter)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz and Rufibach, Kaspar


Lecture Notes - Monograph Series


Institute of Mathematical Statistics




Lutz Dümbgen

Date Deposited:

04 Oct 2013 14:57

Last Modified:

05 Dec 2022 14:17

URI: (FactScience: 49607)

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