Groupe d’études et de recherche en analyse des décisions

A Nonparametric Test for Conditional Independence using Bernstein Density Copulas

Taoufik Bouezmarni

This paper proposes a new nonparametric test for conditional independence which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. We proof that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger non-causality using financial data to test for nonlinear leverage versus volatility feedback effects.