Estimation of Multiresponse Simulation Metamodels Using Control Variates

This paper provides a unified development of the method of control variates for simulation experiments in which the objective is estimation of a multiresponse metamodel---that is, a linear model for an output vector of simulation performance measures expressed in terms of an input vector of decision variables for the target system. In contrast to previous treatments of this topic, we allow both the input and output of the metamodel to be multidimensional so that control variates can be applied to multipopulation, multiresponse simulation experiments. Assuming that the responses and controls are jointly normal with a homogeneous covariance structure across the points of the experimental design, we develop control variates procedures for point and confidence-region estimation and for hypothesis testing on the coefficients of a postulated metamodel. We derive a generalized minimum variance ratio to quantify the maximum efficiency that is achievable with a given set of controls, and we formulate a generalized loss factor to measure the degradation in efficiency that occurs when the optimal control coefficients are estimated by the method of least squares. A detailed example illustrates the application of these results.