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Joint distribution between two or more variables could be influenced by the outcome of a conditioning variable. In this paper, we propose a flexible Wald-type statistic to test for such influence. The test is based on a conditioned multivariate Kendall's tau nonparametric estimator. The asymptotic properties of the test statistic are established under different null hypotheses to be tested for, such as conditional independence or testing for constant conditional dependence. Two simulation studies are presented: The first shows that the estimator proposed and the bandwidth selection procedure perform well. The second presents different bivariate and multivariate models to check the size and power of the test and runs comparisons with previous proposals when appropriate. The results support the contention that the test is accurate even in complex situations and that its computational cost is low. As an empirical application, we study the dependence between some pillars of European Regional Competitiveness when conditioned on the quality of regional institutions. We find interesting results, such as weaker links between innovation and higher education in regions with lower institutional quality. This work was supported by the Spanish Ministry of the Economy and Competitiveness under grants ECO2014-51914-P and PID2019-108718GB-I00; the University of the Basque Country UPV/EHU under grants BETS-UFI11/46, MACLAB-IT93-13 and PES20/44; and the Basque Government under BiRTE-IT1336-19. The first author also acknowledges financial support under PIF16/87 from the University of the Basque Country UPV/EHU. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. |
