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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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

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

First available in Project Euclid: 4 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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