论文标题
通过基于分位数回归的部分Copulas测试有条件独立性
Testing Conditional Independence via Quantile Regression Based Partial Copulas
论文作者
论文摘要
部分copula提供了一种描述两个随机变量$ x $和$ y $之间的依赖性的方法，该$ y $在第三个随机矢量$ z $上，在非参数残差$ u_1 $和$ u_2 $方面。本文通过将部分副群与基于分位数回归的方法相结合，用于估计非参数残留物，从而开发了有条件独立性的非参数测试。我们考虑基于$ u_1 $和$ u_2 $之间的广义相关性的测试统计量，并根据分数回归过程的一致性假设得出其大型样本属性。我们通过一项模拟研究证明，在复杂的数据生成分布中，所得的测试是合理的。此外，在考虑的示例中，该测试在水平和功率方面与其他最先进的有条件独立测试具有竞争力，并且在有条件差异异质性为$ x $和$ y $的情况下，它具有较高的功率。
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 $Z$.
