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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.
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 Conference
Notes WOS:000843190100015 Approved
Call Number UAI @ alexi.delcanto @ Serial 1639
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Author Garcia-Papani, F.; Uribe-Opazo, M.A.; Leiva, V.; Aykroyd, R.G.
Title Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data Type
Year 2017 Publication Stochastic Environmental Research And Risk Assessment Abbreviated Journal Stoch. Environ. Res. Risk Assess.
Volume 31 Issue 1 Pages 105-124
Keywords Asymmetric distributions; Local influence; Matern model; Maximum likelihood methods; Monte Carlo simulation; Non-normality; R software; Spatial data analysis
Abstract Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management.
Address [Garcia-Papani, Fabiana; Uribe-Opazo, Miguel Angel] Univ Estadual Oeste Parana, Postgrad Program Agr Engn, Ctr Exact Sci & Technol, Cascavel, PR, Brazil, Email: fgarciapapani@gmail.com;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1436-3240 ISBN Medium
Area Expedition Conference
Notes WOS:000394278600008 Approved
Call Number UAI @ eduardo.moreno @ Serial 704
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