Strong approximation of empirical copula processes by Gaussian processes
Résumé
This paper investigates the problem of strong approximation of the empirical copula processes for arbitrary dimension, with continuous unknown margins. The idea of the proof is based on the results obtained in Deheuvels et al. (2006), and the theorem of strong approximation for an arbitrary distribution function proved in Csörgo and Horváth (1988). Using these results, we derive the normality for smoothed empirical copula processes and the L.I.L. for empirical copula processes.
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