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Abstract:
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Estimation and testing is studied for functional data with dependent errors, an interesting example of which is the event related potential (ERP). B-spline estimators are formulated for smooth functional trajectories and also the population mean function, the latter shown to be oracally efficient in the sense that it is as efficient as the infeasible estimator were all functional trajectories fully observed without contamination of the infinite moving average errors. The oracle efficiency entails asymptotically correct simultaneous confidence band (SCB) for the mean function, which is useful for making inference on the mean, as confirmed in simulation experiments. When applied to a moderate sized ERP data set, multiple comparison is done by constructing paired SCB from 4 different stimuli, over 3 components N450, N1, N2 separately or simultaneously, leading to interesting findings.
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