Analysis of variance for spatially correlated functional data: Application to brain data

Functional data showing spatial dependence structure occur in many applied fields. For example, in meteorology when curves of temperature are obtained in a monitoring network, or in neurological studies when curves of the electrical activity are recorded in voxels of the brain. The statistical methods for modeling functional data must be adapted to this framework to provide valid inferential procedures. Recently, several works on functional (linear, generalized, additive or semiparametric) models considering correlated functional data have been proposed. Our contribution in this paper is framed in this scenario. Specifically, we show two approaches for carrying out analysis of variance of functional data (FANOVA) when the functions are spatially correlated. These are based on adaptations to the spatial context of two classical techniques given in the literature of FANOVA. To illustrate the methodologies proposed, we analyze a dataset from biomedicine corresponding to curves of evoked potentials obtained under a one-way experimental design