Asymptotic normality of the L-1 error of the Grenander estimator

Authors
Groeneboom, P Hooghiemstra, G Lopuhaa, HP
Citation
P. Groeneboom et al., Asymptotic normality of the L-1 error of the Grenander estimator, ANN STATIST, 27(4), 1999, pp. 1316-1347
Citations number
16
Categorie Soggetti
Mathematics
Journal title
ANNALS OF STATISTICS
ISSN journal
00905364 → ACNP
Volume
27
Issue
4
Year of publication
1999
Pages
1316 - 1347
Database
ISI
SICI code
0090-5364(199908)27:4<1316:ANOTLE>2.0.ZU;2-F
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 re scaled version of the L-1 error of the Grenander estimator, using propertie s of this jump process.