Distribution-free consistent independence tests via center-outward ranks and signs

Understand

This paper investigates the problem of testing independence of two random vectors of general dimensions.

• For this, we give for the first time a distribution-free consistent test.
• Our approach combines distance covariance with the center-outward ranks and signs developed in Hallin (2017).
• In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities.