Abstract
In a wide range of scientific fields the outputs coming from certain measurements often come in form of curves. In this paper we give a solution to the problem of spatial prediction of non-stationary functional data. We propose a new predictor by extending the classical universal kriging predictor for univariate data to the context of functional data. Using an approach similar to that used in univariate geostatistics we obtain a matrix system for estimating the weights of each functional variable on the prediction. The proposed methodology is validated by analyzing a real dataset corresponding to temperature curves obtained in several weather stations of Canada.
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References
Berg C, Forst G (1975) Potential theory on locally compact Abelian groups. Springer, Berlin
Chan K, Oates ASA, Hayes R, Dear B, Peoples M (2006) Agronomic consequences of tractor wheel compaction on a clay soil. Soil Tillage Res 89:13–21
Cressie N (1993) Statistic for spatial data. Wiley, New York
Febrero-Bande M (2008) A present overview on functional data analysis. BEIO 24(1):6–12
Ferraty F, Vieu P (2006) Non-parametric functional data analysis. Theory and practice. Springer, New York
Friman O, Borga M, Lundberg P, Knutsson H (2004) Detection and detrending in fMRI data analysis. Neuroimage 22:645–655
Giraldo R (2009) Geostatistical analysis of functional data. PhD Thesis, Universitat Politécnica de Catalunya
Giraldo R, Delicado P, Mateu J (2011) Ordinary kriging for function-valued spatial data. Environ Ecol Stat 18(3):411–426
Goulard M, Voltz M (1993) Geostatistical interpolation of curves: a case study in soil science. In: Soares A (ed) Geostatistics Tróia ’92, vol 2. Kluwer Academic Press, Boston, pp 805–816
Hollander T, Wolfe D (1999) Nonparametric statistical methods. Wiley, New York
Labat D, Ababou R, Mangin A (1999) Linear and nonlinear input/output models for karstic springflow and flood prediction at different time scales. Stoch Environ Res Risk Assess 13(5):337–364
Mohsin M, Gebhardt A, Pilz J, Spöck G (2012) A new bivariate gamma distribution generated from functional scale parameter with application to drought data. Stoch Environ Res Risk Assess doi:10.1007/s00477-012-0641-6
Oliver J (ed) (2004) Encyclopedia of world climatology. Springer, Dordrecht
Ramsay J, Dalzell C (1991) Some tools for functional data analysis. J R Stat Soc B 53:539–572
Ramsay J, Silverman B (2005) Functional data analysis. Springer, New York
Reyes C (2010) Estimación paramétrica y no paramétrica de la tendencia en datos con dependencia espacial. Un estudio de simulación. Technical report, Universidad Santiago de Compostela
Ruiz-Medina MD, Fernández-Pascual R (2010) Spatiotemporal filtering from fractal spatial functional data sequence. Stoch Environ Res Risk Assess 24:527–538
Ruiz-Medina MD, Salmerón R (2010) Functional maximum-likelihood estimation of arh(p) models. Stoch Environ Res Risk Assess 24:131–146
Salmerón R, Ruiz-Medina MD (2009) Multi-spectral decomposition of functional autoregressive models. Stoch Environ Res Risk Assess 23(3):289–297
Vandenberghe V, Goethals P, Van Griensven A, Meirlaen J, De Pauw N, Vanrolleghem P, Bauwens W (2005) Application of automated measurement stations for continuous water quality monitoring of the Dender River in Flanders, Belgium. Environ Monit Assess 108:85–98
Ver Hoef J, Cressie N (1993) Multivariable spatial prediction. Math Geol 25:219–240
Zhang WJ, Liu G, Dai HQ (2008) Spatiotemporal filtering from fractal spatial functional data sequence. Stoch Environ Res Risk Assess 22(1):123–133
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Caballero, W., Giraldo, R. & Mateu, J. A universal kriging approach for spatial functional data. Stoch Environ Res Risk Assess 27, 1553–1563 (2013). https://doi.org/10.1007/s00477-013-0691-4
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DOI: https://doi.org/10.1007/s00477-013-0691-4