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.

中文翻译：

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Copula 对称性的随机化测试

提出了 copula 可交换性和径向对称性的新非参数检验。测试的新颖之处在于利用与相关对称假设相关的组不变性条件的重采样过程。它们可以被视为对称性随机化测试的可行版本，后者由于边缘的不可观察性而不适用。我们的测试计算简单，渐近控制大小，一致地检测任意形式的不对称，并且不需要调整参数的规范。与涉及乘数自举的现有程序相比，模拟表明具有出色的小样本特性。