Functional regression concurrent model with spatially correlated errors: application to rainfall ground validation

In this paper, we give an extension of the functional regression concurrent model to the case of spatially correlated errors. We propose estimating the spatial correlation structure by using functional geostatistics. The estimation of the regression parameters is carried out by feasible generalized least squares. This modeling approach is motivated by the problem of validating rainfall data retrieved from satellite sensors. In this sense, we use the methodology to study the relationship between satellite and ground rainfall time series recorded in 82 weather stations from Department of Valle del Cauca, Colombia. The model obtained allows predicting pentadal rainfall curves in many sites of the region of interest by using as input the satellite information. A residual analysis shows a good performance of the methodology proposed.