Testing Conditional Independence via Quantile Regression Based Partial Copulas

Lasse Petersen; Niels Richard Hansen

The partial copula provides a method for describing the dependence between two random variables

$X$ and

$Y$ conditional on a third random vector

$Z$ in terms of nonparametric residuals

$U_1$ and

$U_2$ . This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. We consider a test statistic based on generalized correlation between

$U_1$ and

$U_2$ and derive its large sample properties under consistency assumptions on the quantile regression procedure. We demonstrate through a simulation study that the resulting test is sound under complicated data generating distributions. Moreover, in the examples considered the test is competitive to other state-of-the-art conditional independence tests in terms of level and power, and it has superior power in cases with conditional variance heterogeneity of

$X$ and

$Y$ given

$Z$ .

Testing Conditional Independence via Quantile Regression Based Partial Copulas

Abstract