A Projective Approach to Conditional Independence Test for Dependent Processes
A Projective Approach to Conditional Independence Test for Dependent Processes
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DOI：
10.1080/07350015.2020.1826952
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发表时间：
2020-11
影响因子：
3
通讯作者：
Yeqing Zhou;Yaowu Zhang;Liping Zhu
中科院分区：
文献类型：
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作者：
Yeqing Zhou;Yaowu Zhang;Liping Zhu
摘要 条件独立性是许多科学领域的基本概念。在本文中，我们提出了一种投影方法来测量和测试依赖过程的条件独立性的偏离。通过将高维相关过程投影到低维子空间，我们提出的投影方法对过程的维度不敏感。我们证明，在常见的 β 混合条件下，如果这些过程是条件独立的，则我们提出的投影检验统计量是 n 一致的，否则根 n 一致。我们建议使用引导程序来近似检验统计量的渐近零分布。该引导程序的一致性也是严格建立的。我们提出的投影测试的有限样本性能通过对各种替代方案的模拟和测试格兰杰因果关系的经济应用来证明。
Abstract Conditional independence is a fundamental concept in many scientific fields. In this article, we propose a projective approach to measuring and testing departure from conditional independence for dependent processes. Through projecting high-dimensional dependent processes on to low-dimensional subspaces, our proposed projective approach is insensitive to the dimensions of the processes. We show that, under the common β-mixing conditions, our proposed projective test statistic is n-consistent if these processes are conditionally independent and root-n-consistent otherwise. We suggest a bootstrap procedure to approximate the asymptotic null distribution of the test statistic. The consistency of this bootstrap procedure is also rigorously established. The finite-sample performance of our proposed projective test is demonstrated through simulations against various alternatives and an economic application to test for Granger causality.