A Projective Approach to Conditional Independence Test for Dependent Processes
提出一种投影方法，用于测量和检验依赖过程中的条件独立性，通过将高维过程投影到低维子空间，使检验对维度不敏感，并给出渐近性质和自助法过程。
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.