Testing for independence of high-dimensional variables: \(\rho V\)-coefficient based approach (Q2181735)

Consider a high-dimensional normal distributed random vector \(x\) consisting of \(k\) \(p\)-dimensional subvectors \(x_h, h=1,\dots,k\). The problem is to test the hypothesis \(\mathcal{H}_0\) that the stochastic subvectors \(x_1,\dots,x_k\) are mutual independent, against the alternative \(\mathcal{H}_1\) that this is false. Given a sample of independent observations of \(x\), the tests are based on an estimator \(HRV\) of the vector \(\rho V\) of the correlation coefficients of \(\{x_1,\dots,x_k\}\). Several, also asymptotic properties of this estimator and the corresponding test statistic, the test and some variants are shown. Furthermore, in a numerical study, the performance of the proposed test method is evaluated.