@techreport{dbbd2fa2eccf4f71be9bcb15f9ebad30,

title = "Estimating the Variance of the Predictor in Stochastic Kriging",

abstract = "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.",

keywords = "kriging, Gaussian process, predictor variance, plug-in, bootstrap",

author = "J.P.C. Kleijnen and Ehsan Mehdad",

year = "2015",

month = aug,

day = "18",

language = "English",

volume = "2015-041",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}