Cokriging for spatial functional data

• Published in: Journal of Multivariate Analysis
• Main Authors: Nerini, David, Monestiez, Pascal, Manté, Claude
• Other Authors: Laboratoire de MicrobiologiE de Géochimie et d'Ecologie Marines (LMGEM), Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2010
• Subjects: Functional data analysis; RKHS; Functional linear model; Coregionalization; Cokriging; Legendre polynomials; [SDU.OCEAN]Sciences of the Universe [physics]/Ocean; Atmosphere; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]; Antarctic; The Antarctic; Antarctic Ocean; Antarc*; Elephant Seals
• Online Access: https://hal.science/hal-00743881; https://doi.org/10.1016/j.jmva.2009.03.005

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.