Title: Testing conditional mean independence for functional data
Authors: Chung Eun Lee - Baruch College (United States) [presenting]
Xianyang Zhang - Texas A\&M University (United States)
Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States)
Abstract: A new nonparametric conditional mean independence test for a response variable $Y$ and a predictor variable $X$ is proposed where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence, which fully characterizes the conditional mean dependence of $Y$ given $X$ and extends the martingale difference divergence. We define an unbiased estimator of functional martingale difference divergence by using a U-centering approach, and obtain its limiting null distribution under mild assumptions. Since the limiting null distribution is not pivotal, we adopt the wild bootstrap method to estimate the critical value and show the consistency of the bootstrap test. The test does not require a finite-dimensional projection nor assume a linear model, and it does not involve any tuning parameters. Promising finite sample performance is demonstrated via simulations and a real data illustration in comparison with the existing tests.