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- Title
Prediction in regression models with continuous observations.
- Authors
Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
- 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
PREDICTION models; REGRESSION analysis; RANDOM fields; STOCHASTIC processes; KRIGING
- Publication
Statistical Papers, 2024, Vol 65, Issue 4, p1985
- ISSN
0932-5026
- Publication type
Article
- DOI
10.1007/s00362-023-01465-6