TY  - JOUR
SN  - 0304-4149
IS  - 1
KW  - Bahadur-Kiefer approximation; Empirical process theory; 
Generalized uniform empirical process; Level set estimation; Rates of convergence; Test for multimodality
Y1  - 1997///
A1  - Polonik, Wolfgang
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/21331/
N2  - 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.
CY  - Amsterdam
SP  - 1
TI  - Minimum Volume Sets and Generalized Quantile Processes
AV  - public
ID  - heidok21331
JF  - Stochastic processes and their applications
VL  - 69
EP  - 24
PB  - Elsevier
ER  -