Estimating the Variance of the Predictor in Stochastic Kriging

J.P.C. Kleijnen, Ehsan Mehdad

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We study the correct estimation of the true variance of the predictor in stochastic Kriging (SK). First, we obtain macroreplications for a SK metamodel that approximates a single-server simulation model; these macroreplications give independently and identically distributed predictions. This simulation may use common random numbers (CRN). From these macroreplications we conclude that the usual plug-in estimator of the variance signicantly underestimates the true variance. Because macroreplications of practical simulation models are computationally expensive, we next formulate two bootstrap methods that use a single macroreplication: (i) a distribution-free method that resamples simulation replications (within the single macroreplication), and (ii) a parametric method that assumes a Gaussian distribution for the SK predictor, and estimates the (hyper)parameters of that distribution from the single macroreplication. Altogether we recommend distribution-free bootstrapping for the estimation of the SK predictor variance in practical simulation experiments.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages14
Publication statusPublished - 18 Aug 2015

Publication series

NameCentER Discussion Paper


  • kriging
  • Gaussian process
  • predictor variance
  • plug-in
  • bootstrap


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