Cokriging for spatial functional data

Abstract

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

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

“…An increasing body of literature on the geostatistical analysis of functional data is available, either in the stationary [e.g., Goulard and Voltz (1993); Nerini et al (2010); Delicado et al (2010) and references therein] or non-stationary setting (Menafoglio et al 2013;Caballero et al 2013). A relatively rich literature is also available in the field of spatially dependent compositional data [e.g., Tolosana-Delgado et al (2011);Tolosana-Delgado et al (2011);Pawlowsky-Glahn and Olea (2004); Leininger et al (2013) and references therein].…”

Nonparametric M-Estimation for Functional Spatial Data

“…Recently, the functional spatial data has been modeled by two fundamentals regression analysis tools such the cokriging method (see, Nerini et al, 2010) and the nonparametric regression (see, Dabo-Niang and Thiam, 2010) but, it is well known that our robust method has more advantages than the above cited methods by its outlier-resistance properties. In conclusion, we can say that the nonparametric robust analysis in functional spatial data is an important analysis tool and has great impact in practice.…”

Advances in spatial functional statistics

“…There has been a number of adaptations of kriging approaches for spatially correlated functional data. After the pioneering work of Goulard and Voltz (1993), the papers of Delicado et al (2010b) and Nerini et al (2010) have been crucial. Both propose ordinary kriging approaches allowing to predict a curve at an unsampled site under the assumption of stationarity.…”