Prediction in regression models with continuous observations

Detter, Holger, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2024. Prediction in regression models with continuous observations. Statistical Papers 65 , pp. 1985-2009. 10.1007/s00362-023-01465-6

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Abstract

We consider the problem of predicting values of a random process or field satisfying a linear model , where errors 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0932-5026
Date of First Compliant Deposit:	1 July 2023
Date of Acceptance:	1 July 2023
Last Modified:	02 Jul 2024 12:33
URI:	https://orca.cardiff.ac.uk/id/eprint/160757

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