Overcoming negativity problems for Cramer-von Mises variance estimators. (6th October 2008) - Alexopoulos, Christos; Chang, Byeong-Yun; Goldsman, David; Lee, Sungjoo; , William S. Marshall
The weighted Cramer-von Mises (CvM) estimator for the asymptotic variance parameter σ² of a steady-state simulation process has a number of desirable features. For certain weight functions, it is a first-order unbiased estimator of σ², and its variance is lower than that of many other competing estimators. However, the CvM estimator has the unattractive property that it can sometimes assume negative values. This technical note proposes various ways to ameliorate the negativity problem. We find that an effective method is simply that of averaging CvM estimators from a moderate number of contiguous batches of observations from the simulation process.