Independence Test for Functional Data with an Application to Neuroscience

Abstract Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification, while a model-free method only provides a correlation measure which is inadequate to test independence. In this work, we adopt the Hilbert-Schmidt Independence Criterion (HSIC) to measure the dependency between two random functions. We develop a two-step procedure by first pre-smoothing each function based on its discrete and noisy measurements and then applying the HSIC to recovered functions. We propose a new wavelet thresholding method for pre-smoothing and to use Besov-norm-induce d kernels for HSIC. We also provide the corresponding asymptotic analysis. The superior numerical performance of the proposed method over existing ones is demonstrated in a simulation study. Moreover, in a magnetoencephalography (MEG) data application, the functional connectivity patterns identified by the proposed method are more anatomically interpretable than those by existing methods. Bio Rui Miao is a Mathematical Statistician, working at NIH, National Heart, Lung, and Blood Institute, Office of Biostatistics Research, where he develops novel statistical methods for biomedical sciences for NIH intramural research and participates DSMBs in NHLBI funded large clinical trials. His research is focusing on causal inference, reinforcement learning and functional data analysis. Join Zoom Meeting https://duke.zoom.us/j/97335145642?pwd=Pw39xuuMJLTylm1A1yAr6SpMXIwqRq.1 Meeting ID: 973 3514 5642 Passcode: 555382