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Abstract.Spearman’s footrule is a widely used tool to discover the relationship between two continuous random variables, mainly because of its robustness, natural interpretation, and simplicity of calculation. In this article, we propose a new test statistic based on the sum of squares of pairwise Spearman’s footrule, to test the mutual independence of a high dimensional random vector. The large sample properties of the proposed test method are established. Simulation results show that the new test has higher power than existing test methods under some circumstances. An example with real life data is discussed to illustrate the usefulness and effectiveness of the proposed test statistic. [ABSTRACT FROM AUTHOR]

AbstractThere are lots of methods for complete independence test for high-dimensional random vector. However, it is difficult for practitioners to choose a powerful test because the true alternative hypothesis is unknown. Combining the L2-type with the L∞-type test statistic, we propose a rank-based test method. From a technical point of view, the proposed test is distribution-free and consequently the corresponding critical values or p-values can be obtained by Monte Carlo methods. Compared with permutation or bootstrap test methods, the proposed test method saves calculation cost. Simulation results show that the resulting method has excellent performance with finite sample size. We also provide a real data application to demonstrate the practicality and effectiveness of the proposed test method. [ABSTRACT FROM AUTHOR]