Strong approximation of empirical copula processes by Gaussian processes

Salim Bouzebda (1) , Tarek Zari (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

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.

Mots clés: asymptotic theory; Dependence function; strong approximation; asymptotic theory.

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Salim Bouzebda, Tarek Zari. Strong approximation of empirical copula processes by Gaussian processes. 2008. ⟨hal-00340276v2⟩