A0650
Title: Nonlinear interpolation for irregularly observed spatial data: Learning from an additive kriging
Authors: Fumiya Akashi - University of Tokyo (Japan)
Zudi Lu - University of Southampton (United Kingdom) [presenting]
Yan Sun - Utah State University (United States)
Dag Tjoestheim - University of Bergen (Norway)
Abstract: Many applications have stimulated vast interest in theoretical and empirical research on spatial prediction. In fact, the need to obtain accurate predictions from observed data can be found in all scientific disciplines. Kriging, as a method of spatial prediction, was originally coined by a past study for optimal spatial linear prediction under minimum mean squared error after another study on mining grade evaluation. Since then, linear kriging and its extensions, such as generalised linear kriging, have been extensively developed in geostatistics. In general, linear kriging is optimal under Gaussian data assumption, but it often is not, as the Gaussianity for real data is widely violated. A nonlinear kriging is developed via an additive semiparametric structure to learn the nonlinear additive component functions. Theoretical consistency of the estimation is established under mild spatial mixing assumption on the data. Furthermore, the learned nonlinear structures of the component functions are parametrized in threshold (piecewise linear) functions, and hence, a nonlinear kriging is implemented by a co-kriging procedure. Both the simulation data and real data examples demonstrate that our learned nonlinear kriging can significantly outperform the traditional linear kriging for spatial prediction in terms of cross-validation error rates.
