This article considers the problem of testing conditional independence between two random vectors \(bm X\) and \(\bm Y\) given a confounding random vector \(\bm Z\). An exchangeable-pairs framework is introduced through which the conditional independence testing problem is reformulated as a two-sample testing problem. The framework is motivated by ideas from the model-X literature and is based on a fundamental exchangeability property that holds under the null hypothesis of conditional independence. An energy-distance/maximum mean discrepancy type measure is employed on the resulting exchangeable pairs to quantify departures from conditional independence. A consistent estimator of the proposed discrepancy measure is constructed and its theoretical properties are established under general assumptions. A conditional independence test is then developed using this estimator as a test statistic and is calibrated through a suitable resampling procedure. It is shown that the proposed test is consistent against fixed alternatives, possesses nontrivial asymptotic power against local contiguous alternatives, attains the minimax separation rate for detecting alternatives characterized by the proposed discrepancy measure, and remains consistent when the data dimension diverges with the sample size. The effect of estimating the conditional distribution used to generate the exchangeable pairs is also investigated, and condition under which validity and power properties are preserved is established. Extensive simulation studies demonstrate that the proposed procedure performs competitively with some state-of-the-art methods.

翻译：本文考虑了在给定混杂随机向量\(\bm Z\)的情况下，检验两个随机向量\(\bm X\)与\(\bm Y\)之间条件独立性的问题。我们引入了一个可交换对框架，通过该框架将条件独立性检验问题重新表述为两样本检验问题。该框架受模型X文献中的思想启发，基于条件独立性零假设下成立的基本可交换性性质。在所得可交换对上采用能量距离/最大均值差异类型的度量来量化对条件独立性的偏离。我们构建了所提差异度量的一致估计量，并在一般假设下建立了其理论性质。进而，利用该估计量作为检验统计量，通过合适的重抽样过程进行校准，开发了一个条件独立性检验。研究表明，所提检验对固定备择假设具有一致性，对局部邻近备择假设具有非平凡渐近功效，达到了以所提差异度量为特征的备择假设检测的极小化分离速率，并且在数据维度随样本量发散时仍保持一致性。此外，还研究了用于生成可交换对的条件分布估计的影响，并建立了保持有效性和功效性质的条件。大量模拟研究表明，所提方法与一些最先进的方法相比具有竞争力。