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高维经验 Copula 过程：Stute 表示及其应用AI 解读

The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions on the underlying copula, it is shown that Stute’s representation is valid in the following sense: all low-dimensional margins of fixed dimension of the empirical copula process can be approximated by a functional of the low-dimensional…

基于经验 Copula 的高维独立性检验AI 解读

Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature by considering tests that allow to detect higher-order dependencies. The proposed methods are based on connecting the problem to copulas and making use of the Moebius transformation of the empirical copula process; an approach that is…