Minimizing the bias and variance of the gradient estimate in response surface methodology simulation studies

To minimize the variance of the response estimator in response surface methodology (RSM)-based simulations, most users extend the design points to the limits of the subregion under investigation. Our analysis, however, shows that when common pseudorandom numbers are used, this practice likely increases the variance of the estimated gradient. Under the criterion of the variance of the gradient and the Mahalanobis distance function, we show that smaller subregions reduce both the bias and the variance of the estimated gradient. Furthermore, we discuss how users may take advantage of the magnitude of the induced correlations to draw inferences about the search process and to manipulate the subregion size. Our analysis offers a new direction for future research.