Rank-based max-sum tests for mutual independence of high-dimensional random vectors

We consider the problem of testing mutual independence of high-dimensional random vectors, and propose a series of high-dimensional rank-based max-sum tests, which are suitable for high-dimensional data and can be robust to distribution types of the variables, form of the dependence between variables and the sparsity of correlation coefficients. Further, we demonstrate the application of some representative members of the proposed tests on testing cross-sectional independence of the error vectors under fixed effects panel data regression models. We establish the asymptotic properties of the proposed tests under the null and alternative hypotheses, respectively, and then demonstrate the superiority of the proposed tests through extensive simulations, which suggest that they combine the advantages of both the max-type and sum-type high-dimensional rank-based tests. Finally, a real panel data analysis is performed to illustrate the application of the proposed tests.