Estimation of Multiresponse Simulation Metamodels Using Control Variates
统一发展了控制变量法，用于多响应仿真实验中的元模型估计，允许输入和输出均为多维，并给出了点估计、置信域估计和假设检验的程序，通过实例展示了应用。
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.