On the monotonic performance of stochastic kriging predictors

Stochastic kriging (SK) has been recognized as a useful and effective technique for approximating the response surface of a simulation model. In this paper, we analyze the performance of SK metamodels in a fully sequential setting when design points are selected one at a time. We consider both cases when the trend term in the model is either known or estimated and show that the prediction performance of the corresponding optimal SK predictor is monotonically improving as the number of design points increases. Numerical examples are also provided to illustrate our findings.