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An empirical central limit theorem with applications to copulas under weak dependence. (English) Zbl 1333.62207

Summary: We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of conditional copulas and their empirical counterparts are provided.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G07 Density estimation
60F17 Functional limit theorems; invariance principles
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