Spatial functional normal mixed effect approach for curve classification

This paper proposes a spatial functional formulation of the normal mixed effect model for the statistical classification of spatially dependent Gaussian curves, in both parametric and state space model frameworks. Fixed effect parameters are represented in terms of a functional multiple regression model whose regression operators can change in space. Local spatial homogeneity of these operators is measured in terms of their Hilbert–Schmidt distances, leading to the classification of fixed effect curves in different groups. Assuming that the Gaussian random effect curves obey a spatial autoregressive dynamics of order one [SARH(1) dynamics], a second functional classification criterion is proposed in order to detect local spatially homogeneous patterns in the mean quadratic functional variation of Gaussian random effect curve increments. Finally, the two criteria are combined to detect local spatially homogeneous patterns in the regression operators and in the functional mean quadratic variation, under a state space approach. A real data example in the financial context is analyzed as an illustration.