Open Access
May, 1984 The Oscillation Behavior of Empirical Processes: The Multivariate Case
Winfried Stute
Ann. Probab. 12(2): 361-379 (May, 1984). DOI: 10.1214/aop/1176993295


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.


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Winfried Stute. "The Oscillation Behavior of Empirical Processes: The Multivariate Case." Ann. Probab. 12 (2) 361 - 379, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0533.62037
MathSciNet: MR735843
Digital Object Identifier: 10.1214/aop/1176993295

Primary: 60F15
Secondary: 60G17 , 62G05

Keywords: conditional distribution function , copula function , copula process , kernel density estimators , Multivariate empirical process , oscillation modulus , regression function

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
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