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Author Bevilacqua, M.; Camano-Carrillo, C.; Porcu, E.
Title Unifying compactly supported and Matern covariance functions in spatial statistics Type
Year 2022 Publication Journal of Multivariate Analysis Abbreviated Journal J. Multivar. Anal.
Volume 189 Issue Pages 104949
Keywords Gaussian random fields; Generalized wendland model; Fixed domain asymptotics; Sparse matrices
Abstract The Matern family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matern case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported.

More importantly, we show that the proposed covariance family generalizes the Matern model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matern model with an extra-parameter that allows for switching from compactly to globally supported covariance functions.

Our numerical experiments elucidate the speed of convergence of the proposed model to the Matern model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0047-259X ISBN Medium
Area Expedition (up) Conference
Notes WOS:000759649300026 Approved
Call Number UAI @ alexi.delcanto @ Serial 1542
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Author Bachoc, F.; Porcu, E.; Bevilacqua, M.; Furrer, R.; Faouzi, T.
Title Asymptotically equivalent prediction in multivariate geostatistics Type
Year 2022 Publication Bernoulli Abbreviated Journal Bernoulli
Volume 28 Issue 4 Pages 2518-2545
Keywords Cokriging; equivalence of Gaussian measures; fixed domain asymptotics; functional analysis; Generalized Wendland; Matern; spectral analysis
Abstract Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geo-statistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typ-ically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a d-dimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1350-7265 ISBN Medium
Area Expedition (up) Conference
Notes WOS:000843190100015 Approved
Call Number UAI @ alexi.delcanto @ Serial 1639
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