Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/317016 
Year of Publication: 
2023
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 65 [Issue:] 4 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2023 [Pages:] 1985-2009
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract We consider the problem of predicting values of a random process or field satisfying a linear model y(x)=θ⊤f(x)+ε(x), where errors ε(x)are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous observations, we derive expressions for the best linear unbiased predictors and their mean squared error. Our results are also applicable in the case where the derivatives of the process y are available, and either a response or one of its derivatives need to be predicted. The theoretical results are illustrated by several examples in particular for the popular Matérn 3/2 kernel.
Subjects: 
Optimal prediction
Correlated observations
Kriging
Best linear unbiased estimation
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version
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