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 $Z$.

翻译：部分相色板为描述两个随机变量(X美元和Y美元)之间依赖性提供了一种方法,该方法以第三种随机矢量(Z)美元为条件,非参数残留值为1美元和2美元。本文通过将部分相色板与基于量化回归法的估算非参数残留值的方法相结合,对有条件独立性进行了非参数测试。我们认为,根据1美元和2美元之间的普遍关联,根据量化回归程序的一致假设得出其大量样本属性。我们通过模拟研究证明,由此得出的测试在复杂的数据生成分布下是健全的。此外,在所考虑的例子中,在水平和权力方面,该测试与其他最先进的条件独立测试相比具有竞争力,在条件差异性异性为1美元和给以1美元的情况下,该测试具有优势。