title: Minimum Volume Sets and Generalized Quantile Processes
creator: Polonik, Wolfgang
subject: 510
subject: 510 Mathematics
description: 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.
publisher: Elsevier
date: 1997
type: Article
type: info:eu-repo/semantics/article
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/21331/1/beitrag.20.pdf
identifier: DOI:10.11588/heidok.00021331
identifier: urn:nbn:de:bsz:16-heidok-213311
identifier:   Polonik, Wolfgang  (1997) Minimum Volume Sets and Generalized Quantile Processes.  Stochastic processes and their applications, 69 (1).  pp. 1-24.  ISSN 0304-4149     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/21331/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng