Resampling Procedures with Empirical Beta Copulas

Anna Kiriliouk, Johan Segers and Hideatsu Tsukahara
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021018, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: The empirical beta copula is a simple but effective smoother of the empirical copula. Because it is a genuine copula, from which it is particularly easy to sample, it is reasonable to expect that resampling procedures based on the empirical beta copula are expedient and accurate. In this paper, after reviewing the literature on some bootstrap approximations for the empirical copula process, we first show the asymptotic equivalence of several bootstrapped processes related to the empirical and empirical beta copulas. Then we investigate the finite-sample properties of resampling schemes based on the empirical (beta) copula by the Monte Carlo simulation. More specifically, we consider interval estimation for functionals such as the rank correlation coefficients and dependence parameters of several well-known families of copulas. Here, we construct confidence intervals using several methods and compare their accuracy and efficiency. We also compute the actual size and power of symmetry tests based on several resampling schemes for the empirical and empirical beta copulas.

Keywords: Bootstrap approximation; Copula; Empirical beta copula; Empirical copula; Rank correlations; Resampling; Semiparametric estimation; Test of symmetry (search for similar items in EconPapers)
Date: 2021-01-01
Note: In: Pioneering Works on Extreme Value Theory : SpringerBriefs in Statistics, Nobuaki Hoshino, Shuhei Mano, Takaaki Shimura, Springer : Singapore 2021, p. 27-53
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