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A universal kriging predictor for spatially dependent functional data of a Hilbert space. (English) Zbl 1293.62120
Summary: We address the problem of predicting spatially dependent functional data belonging to a Hilbert space, with a functional data analysis approach. Having defined new global measures of spatial variability for functional random processes, we derive a universal kriging predictor for functional data. Consistently with the new established theoretical results, we develop a two-step procedure for predicting georeferenced functional data: first model selection and estimation of the spatial mean (drift), then universal kriging prediction on the basis of the identified model. The proposed methodology is applied to daily mean temperatures curves recorded in the Maritimes Provinces of Canada.

MSC:
62H11 Directional data; spatial statistics
62M20 Inference from stochastic processes and prediction
62M30 Inference from spatial processes
Software:
bootstrap; fda (R); geofd
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References:
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