Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

Abstract

In this work, we consider a nonparametric prediction of a spatiofunctional process observed under a non-random sampling design. The proposed predictor is based on functional regression and depends on two kernels, one of which controls the spatial structure and the other measures the proximity between the functional observations. It can be considered, in particular, as a supervised classification method when the variable of interest belongs to a predefined discrete finite set. The mean square error and almost complete (or sure) convergence are obtained when the sample considered is a locally stationary α-mixture sequence. Numerical studies were performed to illustrate the behavior of the proposed predictor. The finite sample properties based on simulated data show that the proposed prediction method outperformsthe classical predictor which not taking into account the spatial structure.