Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric, rank-based estimators of these coefficients justifies a stopping criterion in an algorithm that searches the collection of all possible groups of variables in a systematic way, from smaller groups to larger ones. The issue that the tolerance level in the stopping criterion should depend on the size of the groups is circumvented by the use of a conditional tail dependence coefficient. Alternatively, such stopping criteria can be based on limit distributions of rank-based estimators of the coefficient of tail dependence, quantifying the speed of decay of joint survival functions. A performance score calculated by ten-fold cross-validation allows the user to select one among the various algorithms and set its tuning parameters in a data-driven way.

中文翻译：

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识别可能同时变大的变量组

识别可能同时较大的变量组相当于找出多元分布的哪些联合尾部依赖系数为正。这些系数的非参数，基于秩的估计量的向量的渐近分布证明了一种算法中的终止标准，该算法以系统的方式搜索从小类到大类的所有可能变量组的集合。通过使用条件尾部依赖系数可以避免在停止标准中的公差水平应取决于组的大小的问题。可替代地，这种停止标准可以基于尾部依赖系数的基于秩的估计器的极限分布，从而量化关节生存函数的衰减速度。