Power Assessment of a New Test of Independence

A new nonparametric test of independence between the components of bivariate random vectors .X; Y / is motivated and evaluated in practice. The test statistics is based on the fact that under independence, every quantile of Y given X D x is constant. This is in contrast to the most commonly used basis that the joint probability density or distribution function ofX and Y , equals to the product of their marginal probability densities or distributions, respectively. Emphasis is given on the small sample power properties of the test. Through numeric simulations with distributional data, the power of the test is benchmarked against standard independence tests, already existing in the literature.