Weighted Multivariate Tests of Independence

Abstract

We present new tests of marginal independence for ℝ^d-valued random vectors. Our tests rely upon weighted Cramér–von Mises-type statistics, which are functionals of the empirical copula process based upon a random sample of size n. We establish a decomposition of this process into asymptotically independent components, and describe the tests which follow from these arguments.

Keywords:

• Copulas
• Cramér–von Mises statistics
• Empirical processes
• Gaussian processes
• Tests of independence

Mathematics Subject Classification:

• Primary 62G10
• Secondary 60F05, 60F10, 60F25, 60J65, 62E20, 62G20, 62G30

Acknowledgments

We thank the referee for a careful reading of our manuscript and his/her insightful comments.