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The oscillation behavior of empirical processes: The multivariate case. (English) Zbl 0533.62037

In this paper sharp finite sample estimates and exact almost sure limit results for local deviations of multivariate empirical processes are derived. These are applied to get exact convergence rates of multivariate kernel density estimators. Also the possibility of studying so-called copula processes is discussed.

MSC:

62G05 Nonparametric estimation
60F15 Strong limit theorems
60G17 Sample path properties
62H12 Estimation in multivariate analysis
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