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August 1999 Asymptotic normality of the $L_1$ error of the Grenander estimator
Piet Groeneboom, Gerard Hooghiemstra, Hendrik P. Lopuhaä
Ann. Statist. 27(4): 1316-1347 (August 1999). DOI: 10.1214/aos/1017938928

Abstract

Groeneboom introduced a jump process that can be used (among other things) to study the asymptotic properties of the Grenander estimator of a monotone density. In this paper we derive the asymptotic normality of a suitably rescaled version of the $L_1$ error of the Grenander estimator, using properties of this jump process.

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Piet Groeneboom. Gerard Hooghiemstra. Hendrik P. Lopuhaä. "Asymptotic normality of the $L_1$ error of the Grenander estimator." Ann. Statist. 27 (4) 1316 - 1347, August 1999. https://doi.org/10.1214/aos/1017938928

Information

Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 1105.62342
MathSciNet: MR1740109
Digital Object Identifier: 10.1214/aos/1017938928

Subjects:
Primary: 62E20, 62G05
Secondary: 60J65, 60J75

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 1999
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