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arXiv · 1110.3437

A Strong Invariance Theorem of the Tail Empirical Copula Processes

Salim Bouzebda·Tarek Zari
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Abstract

We study the behavior of bivariate empirical copula process $\mathbb{G}_n(\cdot,\cdot)$ 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 $\mathbb{G}_n(\cdot,\cdot)$ by a Gaussian process when $k_n/n \searrow γ$ as $n\rightarrow \infty,$ where $0 \leq γ\leq 1.$

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Salim Bouzebda, Tarek Zari. 2011-10-15. A Strong Invariance Theorem of the Tail Empirical Copula Processes. https://doi.org/10.1080/03610926.2011.575514

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