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

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 model. The proposed methodology is applied to daily mean temperatures curves recorded in the Maritimes Provinces of Canada

A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers

“…The aquifer is made up by alluvial material overlain by stiff silty clay and underlain by hard silty clay. The site characterization has been based on stratigraphic information collected at a set of monitoring and pumping wells [Martac and Ptak (2003) and references therein]. The saturated thickness of the aquifer is about 5 m and all boreholes reach the bedrock which forms the impermeable aquifer base.…”

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“…However, in many applied cases, the assumption of a constant mean function is clearly not realistic. To address this problem, there have been a number of contributions dealing with this situation (see Caballero et al 2013;Menafoglio et al 2013;Ignaccolo et al 2014;Reyes et al 2015). In all these cases, the stationarity assumption is relaxed.…”

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