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We propose a model for analyzing replicated functional data
which are spatially correlated. Our research, stems from the need for
accurate estimation of spatio-temporal fields by summarising information
observed over several replicates. Our framework generalizes the existing
framework of spatio-temporal regression model with partial differential
equations regularisation (ST-PDE) approach and thus can accommodate
spatially dependent functions or time dependent surfaces embedded in
manifolds and irregular boundaries. This need has emerged for a study on
classification of brain signals based on the difference in visual
stimulus. Analytically, we show that the estimators of composite
spatio-temporal field is relatively more efficient than existing
estimators. The proposed method is thoroughly compared via simulation
studies to existing spatio-temporal functional techniques and is applied
to the analysis of the EEG data on brain signals to provide a composite
temporally varying brain map over several replications. |