Authors: Dette, Holger
Pepelyshev, Andrey
Zhigljavsky, Anatoly
Title: Prediction in regression models with continuous observations
Language (ISO): en
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.
Subject Headings: optimal prediction
best linear unbiased estimation
correlated observations
Issue Date: 2019
Appears in Collections:Sonderforschungsbereich (SFB) 823

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