The Annals of Probability

The Oscillation Behavior of Empirical Processes: The Multivariate Case

Winfried Stute

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Abstract

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.

Article information

Source
Ann. Probab., Volume 12, Number 2 (1984), 361-379.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993295

Digital Object Identifier
doi:10.1214/aop/1176993295

Mathematical Reviews number (MathSciNet)
MR735843

Zentralblatt MATH identifier
0533.62037

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60G17: Sample path properties 62G05: Estimation

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

Citation

Stute, Winfried. The Oscillation Behavior of Empirical Processes: The Multivariate Case. Ann. Probab. 12 (1984), no. 2, 361--379. doi:10.1214/aop/1176993295. https://projecteuclid.org/euclid.aop/1176993295


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