A Class of Robust Independence Tests Based on Weighted Integrals of Empirical Characteristic Functions

Abstract

In this paper, we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions. By letting weight functions be probability density functions of a class of special distributions, the proposed test statistics have simple closed forms and do not require moment conditions on the random vectors. Moreover, we derive the asymptotic distributions of the test statistics under the null hypothesis. The proposed testing method is computationally feasible and easy to implement. Based on a data-driven bandwidth selection method, Monte Carlo simulation studies indicate that our tests have a relatively good performance compared with the competitors. A real data example is also presented to illustrate the application of our tests.