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This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g., all pairwise Kendall’s τ) between the components vanish, we are interested in the (null) hypothesis that all pairwise associations do not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in the high-dimensional regime,…

重尾总体样本相关矩阵特征值的极限分布AI 解读

Consider a p-dimensional population x∈Rp with i.i.d. coordinates that are regularly varying with index α∈(0,2). Since the variance of x is infinite, the diagonal elements of the sample covariance matrix Sn=n−1 ∑ i=1nxixi′ based on a sample x1,…,xn from the population tend to infinity as n increases and it is of interest to use instead the sample correlation matrix Rn={diag(Sn)}−1/2Sn{diag(Sn)}−1/2. This paper finds the limiting distributions of the eigenvalues of Rn when…