Nonparametric tests of independence using copula-based Renyi and Tsallis divergence measures

‎We introduce new nonparametric independence tests based on R\'enyi and Tsallis divergence measures and copula density function‎. ‎These tests reduce the complexity of calculations because they only depend on the copula density‎. ‎The copula density estimated using the local likelihood probit-transformation method is appropriate for the identification of independence‎. ‎Also‎, ‎we present the consistency of the copula-based R\'enyi and Tsallis divergence measures estimators that are considered as test statistics‎. ‎A simulation study is provided to compare the empirical power of these new tests with the independence test based on the empirical copula‎. ‎The simulation results show that the suggested tests outperform in weak dependency‎. ‎Finally‎, ‎an application in hydrology is presented‎.