A1981
Title: A doubly projected test for conditional independence with high-dimensional dependent data
Authors: Songyen Chen - National Chengchi University (Taiwan) [presenting]
Tzee-Ming Huang - National Chengchi Univerisity (Taiwan)
Abstract: The problem of testing conditional independence is crucial in statistics, econometrics, and modern machine learning, yet it remains challenging in the presence of high-dimensional dependencies. A conditional independence testing framework is addressed under high-dimensional dependent data. A self-normalized type test statistic is proposed that integrates time series block smoothing, sample splitting, and flexible machine learning techniques satisfying suitable convergence rates. The key insight of the framework is that the double projection strategy maps the conditional independence problem into a family of unconditional covariate weighted orthogonality conditions, bypassing the additive noise exogeneity condition commonly required by conventional residual based conditional independence tests. In particular, the proposed test is capable of detecting both linear and nonlinear conditional dependence structures. Under mild conditions, and allowing both the dimension of the covariates and the sample size to diverge, the test statistic is shown to be asymptotically pivotal under the null, and asymptotic local power properties are established against alternatives. Simulation studies demonstrate satisfactory finite sample performance. An empirical application illustrates the usefulness of the proposed approach in testing for high-dimensional Granger non causality.
