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.
Publié le : 1999-08-14
Classification:
Brownian motion with quadratic drift,
central limit theorem,
concave majorant,
isotonic estimation,
jump process,
$L_1$-norm,
monotone density,
62E20,
62G05,
60J65,
60J75
@article{1017938928,
author = {Groeneboom, Piet and Hooghiemstra, Gerard and Lopuha\"a, Hendrik P.},
title = {Asymptotic normality of the $L\_1$ error of the Grenander
estimator},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1316-1347},
language = {en},
url = {http://dml.mathdoc.fr/item/1017938928}
}
Groeneboom, Piet; Hooghiemstra, Gerard; Lopuhaä, Hendrik P. Asymptotic normality of the $L_1$ error of the Grenander
estimator. Ann. Statist., Tome 27 (1999) no. 4, pp. 1316-1347. http://gdmltest.u-ga.fr/item/1017938928/