Cokriging for spatial functional data
This work proposes to generalize the method of kriging when data are spatially sampled curves. A spatial functional linear model is constructed including spatial dependencies between curves. Under some regularity conditions of the curves, an ordinary kriging system is established in the infinite dimensional case. From a practical point-of-view, the decomposition of the curves into a functional basis boils down the problem of kriging in infinite dimension to a standard cokriging on basis coefficients. The methodological developments are illustrated with temperature profiles sampled with dives of elephant seals in the Antarctic Ocean. The projection of sampled profiles into a Legendre polynomial basis is performed with a regularization procedure based on spline smoothing which uses the variance of the sampling devices in order to estimate coefficients by quadrature.
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Volume (Year): 101 (2010)
Issue (Month): 2 (February)
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- Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
- Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
- Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
- Pearce, N.D. & Wand, M.P., 2006. "Penalized Splines and Reproducing Kernel Methods," The American Statistician, American Statistical Association, vol. 60, pages 233-240, August.
- Meiring, Wendy, 2007. "Oscillations and Time Trends in Stratospheric Ozone Levels: A Functional Data Analysis Approach," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 788-802, September.
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