Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ and Kendall’s $$\tau $$

Abstract

Inspired by the correlation matrix and based on the generalized Spearman’s $$\rho $$ and Kendall’s $$\tau $$ between random variables proposed in Lu et al. ( J Nonparametr Stat 30(4):860–883, 2018), $$\rho $$ -matrix and $$\tau $$ -matrix are suggested for multivariate data sets. The matrices are used to construct the $$\rho $$ -measure and the $$\tau $$ -measure among random vectors with statistical estimation and the asymptotic distributions under the null hypothesis of independence that produce the nonparametric tests of independence for multiple vectors. Simulation results demonstrate that the proposed tests are powerful under different grouping of the investigated random vector. An empirical application to detecting dependence of the closing price of a portfolio of stocks in NASDAQ also illustrates the applicability and effectiveness of our provided tests. Meanwhile, the corresponding measures are applied to characterize strength of interdependence of that portfolio of stocks during the recent two years.