A statistical procedure to determine if the dependence structure of a multivariate random vector belongs or not to the general class of elliptical copulas has been proposed by Jaser et al. (Depend Model 5:330–353, 2017). Their test exploits the fact that when the copula of a multivariate population is elliptical, the theoretical Kendall and Blomqvist dependence measures of each pair are the same. Under a setup where the marginal distributions are known, they based their decision rule on the asymptotic distribution of the proposed test statistic, which is chi-squared. In this paper, the restrictive assumption of known marginals is relaxed by the use of ranks. In addition, new test statistics are proposed and their p-values are computed from suitably adapted bootstrap replicates based on the form of their limit under the null hypothesis. Unlike Jaser et al.’s test, the proposed procedures keep their nominal level well when the dimension exceeds two. It is also shown that the new tests have good power properties against several types of alternatives to copula ellipticity.

中文翻译：

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关于多元元椭圆度的非参数检验

Jaser 等人提出了一种统计程序，用于确定多元随机向量的相关结构是否属于椭圆 copula 的一般类别。（取决于模型 5：330-353，2017 年）。他们的测试利用了这样一个事实，即当多元总体的 copula 是椭圆时，每对的理论 Kendall 和 Blomqvist 依赖度量是相同的。在边际分布已知的设置下，他们的决策规则基于提议的检验统计量的渐近分布，即卡方。在本文中，已知边际的限制性假设通过使用秩而放宽。此外，还提出了新的测试统计数据，并且它们的 p 值是根据它们在零假设下的极限形式从适当调整的自举复制中计算出来的。与 Jaser 等人的测试不同，当维度超过 2 时，所提出的程序可以很好地保持其标称水平。还表明，新的测试对于 copula 椭圆度的几种替代方法具有良好的功率特性。