A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space

Code:
34/2012
Title:
A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space
Date:
Tuesday 4th September 2012
Author(s):
Menafoglio, A.; Dalla Rosa, M.; Secchi, P.
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Abstract:
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 dichotomy model, sum of deterministic drift and stochastic residuals. The proposed methodology is tested by means of a simulation study and finally applied to daily mean temperatures curves aiming at reconstructing the space-time field of temperatures of Canada s Maritimes Provinces.