Adaptive Minimal Confidence Region Rule for Multivariate Initialization Bias Truncation in Discrete-event Simulations

Initialization bias truncation is critically important for system performance assessment and warm-up length estimation in discrete-event simulations. Most of the existing methods are for univariate signals, while multivariate truncation has been rarely studied. To fill such gap, this paper proposes an efficient method, called adaptive minimal confidence region rule (AMCR) for multivariate initialization bias truncation. It determines the truncation point by minimizing the modified confidence volume with a tuning parameter for the mean estimate. An elbow method is developed for adaptive selection of the tuning parameter. Theoretical properties of the AMCR rule for both data with and without autocorrelations have been derived for justification and practical guidance. The effectiveness and superiority of the AMCR rule over other existing approaches have been demonstrated through thorough numerical studies and real application. Supplementary materials for this article are available online.