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Asymptotic total variation tests for copulas. (English) Zbl 1331.62282

This work introduces a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The new test extends the standard Kolmogorov-Smirnov type test for copulas in the sense that while the Kolmogorov-Smirnov test takes the supremum of the empirical copula process indexed by orthants, the new test is based on the empirical copula process indexed by families of \(L_n\) disjoint boxes with \(L_n\) tending to infinity at an adequate slower rate than \(n.\) At such rate the underlying empirical process does not converge. However, the critical values of the new test statistics can be consistently estimated by their nonparametric bootstrap counterparts. It is shown else that for parametric hypothesis, i.e., when the copula is indexed by a parameter, the new test works well. Some applications are presented and simulations show that the power of the new test is consistently higher than the power of the standard Kolmogorov-Smirnov or the Cramér-von Mises test for copula on the examples worked in the paper.

MSC:

62H15 Hypothesis testing in multivariate analysis
62G09 Nonparametric statistical resampling methods
62G10 Nonparametric hypothesis testing

Software:

TwoCop
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References:

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