A Strong Invariance Theorem of the Tail Empirical Copula Processes |
| |
| Authors: | Salim Bouzebda Tarek Zari |
| |
| Institution: | 1. L.S.T.A. , Université Pierre et Marie Curie-Paris VI , Parisand L.M.A.C. Université Technologie de Compiègne, Francesalim.bouzebda@upmc.fr;3. Université Hassan II – FSJES A?n Sbaa , Casablanca , Marocco |
| |
| Abstract: | We study the behavior of bivariate empirical copula process 𝔾 n (·, ·) on pavements 0, k n /n]2 of 0, 1]2, where k n is a sequence of positive constants fulfilling some conditions. We provide a upper bound for the strong approximation of 𝔾 n (·, ·) by a Gaussian process when k n /n↘γ as n → ∞, where 0 ≤ γ ≤1. |
| |
| Keywords: | Empirical copula processes Gaussian processes Rates of convergences Strong invariance principles |
|
|
