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.

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

MENAFOGLIO, ALESSANDRA;SECCHI, PIERCESARE
2012-01-01

Abstract

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.
2012
Book of Abstracts
978-88-6129-882-8
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/748993
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