Prediction of non-stationary functional data: Universal Kriging in a Hilbert space

In an increasing number of studies, collected data are curves; when functional data are spatially dependent, the problem of prediction assumes a key role. In this work we deal with spatially distributed functional data proposing an extension of some geostatistical tools to non-stationary functional random fields, with a Functional Data Analysis approach. An extension of the Universal Kriging method to elements of a Hilbert space is proposed, in a coherent frame of definitions and assumptions. Consistently with these new theoretical results, a method for prediction of non-stationary spatial dependent functional data is proposed and then developed in three steps: model selection for the drift term, decomposition of the original process into a deterministic term (the drift) and a residual stochastic process, Universal Kriging prediction. The proposed procedure is applied to daily mean temperatures curves observed in 35 meteorological stations located in Canada's Maritimes Provinces.