Statistical Tests for Cross-Validation of Kriging Models

Jack Kleijnen, W.C.M. van Beers

Research output: Working paperDiscussion paperOther research output

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Abstract

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confi…dence intervals. We may wish to avoid extrapolation, which we de…fine
as prediction of the output for a point that is a vertex of the convex hull of the
given input combinations. Moreover, we may use bootstrapping to estimate the
true variance of the Kriging predictor. The resulting tests (with or without extrapolation or bootstrapping) have type-I and type-II error probabilities, which
we estimate through Monte Carlo experiments. To illustrate the application of
our tests, we use an example with two inputs and the popular borehole example
with eight inputs.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages42
Volume2019-022
Publication statusPublished - 29 May 2019

Publication series

NameCentER Discussion Paper
Volume2019-022

Fingerprint

Kriging
Statistical test
Cross-validation
Bootstrapping
Extrapolation
Type II error
Monte Carlo Experiment
Error Probability
Convex Hull
Estimate
Confidence interval
Predictors
Model
Prediction
Output
Vertex of a graph

Keywords

  • validation
  • cross-validation
  • Kriging
  • Gaussian process
  • extrapolation
  • convex hull
  • Monte Carlo Technique

Cite this

Kleijnen, J., & van Beers, W. C. M. (2019). Statistical Tests for Cross-Validation of Kriging Models. (CentER Discussion Paper; Vol. 2019-022). Tilburg: CentER, Center for Economic Research.
Kleijnen, Jack ; van Beers, W.C.M. / Statistical Tests for Cross-Validation of Kriging Models. Tilburg : CentER, Center for Economic Research, 2019. (CentER Discussion Paper).
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Kleijnen, J & van Beers, WCM 2019 'Statistical Tests for Cross-Validation of Kriging Models' CentER Discussion Paper, vol. 2019-022, CentER, Center for Economic Research, Tilburg.

Statistical Tests for Cross-Validation of Kriging Models. / Kleijnen, Jack; van Beers, W.C.M.

Tilburg : CentER, Center for Economic Research, 2019. (CentER Discussion Paper; Vol. 2019-022).

Research output: Working paperDiscussion paperOther research output

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Kleijnen J, van Beers WCM. Statistical Tests for Cross-Validation of Kriging Models. Tilburg: CentER, Center for Economic Research. 2019 May 29. (CentER Discussion Paper).