Estimating the variance of the predictor in stochastic Kriging

• In practice, the parameters of a Kriging metamodel must be estimated.
• In practice, these estimated parameters are plugged into the predictor formula.
• This plugging-in creates bias in the estimator of the predictor variance.
• We present three methods for estimation of the predictor variance.
• We compare these methods through experiments with M/M/1 simulation model.

We study the 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 significantly 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.