A new test of independence for bivariate observations

This research contributes a new methodological advance on bivariate independence hypothesis testing. It is based on the property that under independence, every quantile of Y given X=x is constant. Apart from the asymptotic distributions of the test statistic under the null and alternative hypotheses, this work establishes their first order Edgeworth expansion. This is used to construct a bandwidth selection rule, designed to maximize power while the size is controlled by a given significance level. Finally, numerical evidence is given on the test's benefits against standard independence tests, frequently encountered in the literature.