The Oscillation Behavior of Empirical Processes: The Multivariate Case

Open Access

1 May 1984

journal article
Published by Institute of Mathematical Statistics in The Annals of Probability

Vol. 12 (2) , 361-379
https://doi.org/10.1214/aop/1176993295

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.

Keywords

MULTIVARIATE EMPIRICAL PROCESS
OSCILLATION MODULUS
COPULA FUNCTION
KERNEL DENSITY ESTIMATORS
COPULA PROCESS
CONDITIONAL DISTRIBUTION FUNCTION
REGRESSION FUNCTION

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