A Strong Invariance Theorem of the Tail Empirical Copula Processes
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 $0 \leq γ\leq 1.$
math.ST↗