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Title: Testing the conditional mean independence for functional data Authors:  Xiaofeng Shao - University of Illinois at Urbana-Champaign (United States) [presenting]
Chung Eun Lee - University of Tennessee, Knoxville (United States)
Xianyang Zhang - Texas A\&M University (United States)
Abstract: A new nonparametric conditional mean independence test is introduced for a response variable $Y$ and a predictor variable $X$ where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence (FMDD), which fully characterizes the conditional mean dependence of $Y$ given $X$ and extends a previous MDD. We define an unbiased estimator of FMDD 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. Promising finite sample performance is demonstrated via simulations and a real data illustration in comparison with several existing tests.