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Randomization tests of copula symmetry. (English) Zbl 1462.62297

Summary: New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of marginals. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared with existing procedures involving the multiplier bootstrap.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G10 Nonparametric hypothesis testing

Software:

TwoCop
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References:

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