We derive sharp finite sample estimates and exact almost sure limit results for local deviations of multivariate empirical processes. These are useful for obtaining, e.g., exact convergence rates of multivariate kernel density estimators. It is also indicated how local properties of multivariate empirical processes may be used to study various problems in nonparametric multivariate analysis.
Publié le : 1984-05-14
Classification:
Multivariate empirical process,
oscillation modulus,
copula function,
kernel density estimators,
copula process,
conditional distribution function,
regression function,
60F15,
60G17,
62G05
@article{1176993295,
author = {Stute, Winfried},
title = {The Oscillation Behavior of Empirical Processes: The Multivariate Case},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 361-379},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993295}
}
Stute, Winfried. The Oscillation Behavior of Empirical Processes: The Multivariate Case. Ann. Probab., Tome 12 (1984) no. 4, pp. 361-379. http://gdmltest.u-ga.fr/item/1176993295/