A note on the distribution of the partial correlation coefficient with nonparametrically estimated marginal regressions

There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have been overlooked, its distribution only having been investigated in some simple parametric instances. The present note shows that an easy to apply permutation test based on the sample partial correlation with nonparametrically estimated marginal regressions has good large and small sample properties.