eprintid: 21331
rev_number: 11
eprint_status: archive
userid: 2326
dir: disk0/00/02/13/31
datestamp: 2016-06-16 07:39:00
lastmod: 2016-11-08 18:25:30
status_changed: 2016-06-16 07:39:00
type: article
metadata_visibility: show
creators_name: Polonik, Wolfgang
title: Minimum Volume Sets and Generalized Quantile Processes
subjects: 510
divisions: 110400
keywords: Bahadur-Kiefer approximation; Empirical process theory; 
Generalized uniform empirical process; Level set estimation; Rates of convergence; Test for multimodality
abstract: Minimum volume sets in classes C of subsets of the d-dimensionalEuclidean space can be used as estimators of level sets of a density. By usingempirical process theory consistency results and rates of convergence forminimum volume sets are given which depend on entropy conditions on C .The volume of the minimum volume sets itself, which can be used for robustestimation of scale, can be considered as a generalized quantile process inthe sense of Einmahl and Mason (1992). Bahadur-Kiefer approximations forgeneralized quantile processes are given which generalize classical resultson the one-dimensional quantile process. Rates of convergence of minimumvolume sets can be used to obtain Bahadur-Kiefer approximations and viceversa. A generalization of the minimum volume approach to regressionproblems and spectral analysis is presented.
date: 1997
publisher: Elsevier
id_scheme: DOI
id_number: 10.11588/heidok.00021331
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 20
ppn_swb: 1653753749
own_urn: urn:nbn:de:bsz:16-heidok-213311
language: eng
bibsort: POLONIKWOLMINIMUMVOL1997
full_text_status: public
publication: Stochastic processes and their applications
volume: 69
number: 1
place_of_pub: Amsterdam
pagerange: 1-24
issn: 0304-4149
citation:   Polonik, Wolfgang  (1997) Minimum Volume Sets and Generalized Quantile Processes.  Stochastic processes and their applications, 69 (1).  pp. 1-24.  ISSN 0304-4149     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21331/1/beitrag.20.pdf