This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation of the \textit{weighted partial copula}, (ii) the regions of rejection are computed using a bootstrap procedure which mimics conditional independence by generating samples from the product measure of the estimated conditional marginals. Under conditional independence, the weak convergence of the \textit{weighted partial copula proces}s is established when the marginals are estimated using a smoothed local linear estimator. Finally, an experimental section demonstrates that the proposed test has competitive power compared to recent state-of-the-art methods such as kernel-based test.
翻译:本文介绍了用于测试有条件独立性的\ textit{ 加权部分 Conula} 函数。 拟议的测试程序来自这两个元素:(一) 测试统计是一个明确的 Cramer- von Mises 转换 \ textit{ 加权部分 Copula}, (二) 拒绝区域是使用一个靴套程序来计算,该程序通过从估计有条件边际的产品量测中生成样本来模仿有条件独立。 在有条件独立的情况下,当边际点使用平滑的本地线性估计仪估算时,确定 \ textit{ 加权部分 Cocula Proce} 的趋同性较弱。 最后, 实验部分显示, 拟议的测试与最近最先进的方法如内核测试相比, 具有竞争力 。