Cokriging based on curves: Prediction and estimation of the prediction variance
by Ramón Giraldo.
Kriging and cokriging and their several related versions are widely known and used for spatial data. However, when the spatial data are functions a bridge
between functional data analysis and geostatistics has to be built. I give an overview to cokriging analysis and multivariable spatial prediction to
the case where the observations at each sampling location consist of
samples of random functions. I extend classical cokriging multivariable geostatistical methods to the functional context. Our
cokriging method predicts one variable at a time as in a classical
multivariable sense, but considering as auxiliary information curves
instead of vectors. I also give and overview of multivariable
kriging to the functional context where is defined a predictor of a whole
curve based on samples of curves located at a neighborhood of the
prediction site. In both cases a non-parametric approach based on
basis function expansion is used to estimate the parameters, and I
prove that both proposals coincide when using such an approach. A
linear model of coregionalization is used to define the spatial
dependence among the coefficients of the basis functions, and
therefore for estimating the functional parameters. As an
illustration the methodological proposals are applied to analyze two
real data sets corresponding to average daily temperatures measured
at 35 weather stations located in the Canadian Maritime Provinces,
and penetration resistance data collected at 32 sampling sites of an
Basis Functions, Cross-Validation, Functional
Linear Model, Linear Model of Coregionalization, Multivariable Cokriging
Ramón Giraldo, email@example.com
Mark Greenwood, firstname.lastname@example.org
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