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Radial basis functions with compact support for multivariate geostatistics

Author:
Porcu, Emilio, Daley, Daryl J., Buhmann, Martin, Bevilacqua, Moreno
Source:
Stochastic environmental research and risk assessment 2013 v.27 no.4 pp. 909-922
ISSN:
1436-3240
Subject:
covariance, data collection, geostatistics, models, prediction, temperature, Pacific States
Abstract:
Matrix-valued radially symmetric covariance functions (also called radial basis functions in the numerical analysis literature) are crucial for the analysis, inference and prediction of Gaussian vector-valued random fields. This paper provides different methodologies for the construction of matrix-valued mappings that are positive definite and compactly supported over the sphere of a d-dimensional space, of a given radius. In particular, we offer a representation based on scaled mixtures of Askey functions; we also suggest a method of construction based on B-splines. Finally, we show that the very appealing convolution arguments are indeed effective when working in one dimension, prohibitive in two and feasible, but substantially useless, when working in three dimensions. We exhibit the statistical performance of the proposed models through simulation study and then discuss the computational gains that come from our constructions when the parameters are estimated via maximum likelihood. We finally apply our constructions to a North American Pacific Northwest temperatures dataset.
Agid:
206901