Prediction in regression models with continuous observations

Holger Dette (), Andrey Pepelyshev () and Anatoly Zhigljavsky ()
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Holger Dette: Ruhr-Universität Bochum
Andrey Pepelyshev: Cardiff University
Anatoly Zhigljavsky: Cardiff University

Statistical Papers, 2024, vol. 65, issue 4, No 4, 1985-2009

Abstract: Abstract We consider the problem of predicting values of a random process or field satisfying a linear model $$y(x)=\theta ^\top f(x) + \varepsilon (x)$$ y ( x ) = θ ⊤ f ( x ) + ε ( x ) , where errors $$\varepsilon (x)$$ 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.

Keywords: Optimal prediction; Correlated observations; Kriging; Best linear unbiased estimation; 62M20; 60G25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01465-6

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