The Annals of Statistics

Asymptotic normality of the $L_1$ error of the Grenander estimator

Piet Groeneboom, Gerard Hooghiemstra, and Hendrik P. Lopuhaä

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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.

Article information

Source
Ann. Statist., Volume 27, Number 4 (1999), 1316-1347.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017938928

Digital Object Identifier
doi:10.1214/aos/1017938928

Mathematical Reviews number (MathSciNet)
MR1740109

Zentralblatt MATH identifier
1105.62342

Subjects
Primary: 62E20: Asymptotic distribution theory 62G05: Estimation
Secondary: 60J65: Brownian motion [See also 58J65] 60J75: Jump processes

Keywords
Brownian motion with quadratic drift central limit theorem concave majorant isotonic estimation jump process $L_1$-norm monotone density

Citation

Groeneboom, Piet; Hooghiemstra, Gerard; Lopuhaä, Hendrik P. Asymptotic normality of the $L_1$ error of the Grenander estimator. Ann. Statist. 27 (1999), no. 4, 1316--1347. doi:10.1214/aos/1017938928. https://projecteuclid.org/euclid.aos/1017938928


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