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Title: On some resampling procedures with the empirical Beta copula Authors:  Hideatsu Tsukahara - Seijo University (Japan) [presenting]
Johan Segers - Universite catholique de Louvain (Belgium)
Anna Kiriliouk - University of Namur (Belgium)
Abstract: Because of many nice properties of the empirical beta copula, it is reasonable to expect that our smoothing procedure might also have a beneficial effect on the accuracy of resampling schemes for the empirical copula process. More specifically, testing procedures based on the empirical copula typically rely on the bootstrap for the computation of the critical values of the test statistic. For finite samples, the accuracy is often not very good: the actual size of the test may differ greatly from the nominal one. We first show the asymptotic equivalence of several related bootstrapped processes. Then we investigate the accuracy of the bootstrap resampling schemes based on the empirical beta copulas with small sample sizes; we consider confidence intervals for some functionals such as rank correlation coefficients and dependence parameters of several well-known copula families, and goodness-of-fit testing problems including testing exchangeability. And we compare the performance of three methods: standard asymptotic approximation, standard bootstrapping and resampling from the empirical beta copula.