Overlapping variance estimators for simulation
成果类型：
Article
署名作者：
Alexopoulos, Christos; Argon, Nilay Tank; Goldsman, David; Tokol, Gamze; Wilson, James R.
署名单位：
University System of Georgia; Georgia Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; North Carolina State University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0475
发表日期：
2007
页码：
1090-1103
关键词：
摘要：
To estimate the variance parameter (i.e., the sum of covariances at all lags) for a steady-state simulation output process, we formulate certain statistics that are computed from overlapping batches separately and then averaged over all such batches. We form overlapping versions of the area and Cramer-von Mises estimators using the method of standardized time series. For these estimators, we establish (i) their limiting distributions as the sample size increases while the ratio of the sample size to the batch size remains fixed; and (ii) their mean-square convergence to the variance parameter as both the batch size and the ratio of the sample size to the batch size increase. Compared with their counterparts computed from nonoverlapping batches, the estimators computed from overlapping batches asymptotically achieve reduced variance while maintaining the same bias as the sample size increases; moreover, the new variance estimators usually achieve similar improvements compared with the conventional variance estimators based on nonoverlapping or overlapping batch means. In follow-up work, we present several analytical and Monte Carlo examples, and we formulate efficient procedures for computing the overlapping estimators with only order-of-sample-size effort.