Ordinary kriging for function-valued spatial data

In various scientific fields properties are represented by functions varying over space. In this paper, we present a methodology to make spatial predictions at non-data locations when the data values are functions. In particular, we propose both an estimator of the spatial correlation and a functional kriging predictor. We adapt an optimization criterion used in multivariable spatial prediction in order to estimate the kriging parameters. The curves are pre-processed by a non-parametric fitting, where the smoothing parameters are chosen by cross-validation. The approach is illustrated by analyzing real data based on soil penetration resistances.