In: Stochastic processes and their applications, 69 (1997), Nr. 1. pp. 1-24. ISSN 0304-4149
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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.
Document type: | Article |
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Journal or Publication Title: | Stochastic processes and their applications |
Volume: | 69 |
Number: | 1 |
Publisher: | Elsevier |
Place of Publication: | Amsterdam |
Date Deposited: | 16 Jun 2016 07:39 |
Date: | 1997 |
ISSN: | 0304-4149 |
Page Range: | pp. 1-24 |
Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Uncontrolled Keywords: | Bahadur-Kiefer approximation; Empirical process theory; Generalized uniform empirical process; Level set estimation; Rates of convergence; Test for multimodality |
Series: | Beiträge zur Statistik > Beiträge |