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Title: Inference for dependent error functional data with application to event related potentials Authors:  Kun Huang - Tsinghua University (China) [presenting]
Sijie Zheng - Tsinghua University (China)
Lijian Yang - Tsinghua University (China)
Abstract: Estimation and testing is studied for functional data with temporally dependent errors, an interesting example of which is the event-related potential (ERP). B-spline estimators are formulated for individual smooth trajectories and their population mean as well. The mean estimator is shown to be oracally efficient in the sense that it is as efficient as the infeasible mean estimator if all trajectories had been fully observed without contamination of errors. The oracle efficiency entails asymptotically correct simultaneous confidence band (SCB) for the mean function, which is useful for making inference on the global shape of the mean. Extensive simulation experiments with various time series errors and functional principal components confirm the theoretical conclusions. For a moderate sized ERP data set, multiple comparisons is done by constructing paired SCBs among 4 different stimuli, over 3 components N450, N1, N2 separately or simultaneously, leading to interesting findings.