Abstract: Numerous studies in neuroscience have demonstrated links between brain spectral activity and cognition, sleep, disease diagnosis and treatment outcomes. In this paper, we study the variation of spectral activity across the brain cortical surface. We rigorously develop the concept of a location-dependent temporal spectrum for a wide class of spatio-temporal processes. Under the proposed asymptotic framework, the location-dependent spectrum can be estimated consistently. A non-parametric smoothing method is proposed and, under regularity conditions, is shown to be asymptotically normal and mean-square consistent. The paper concludes with an analysis of an event-related optical signal (EROS)data recorded from a single subject during a spatial-verbal Stroop task.
Key words and phrases: Event-related optical signal (EROS), kernel-smoothing, Spatio-temporal random process, spectrum.