Title: Overcoming negativity problems for Cramer-von Mises variance estimators

Authors: Christos Alexopoulos, Byeong-Yun Chang, David Goldsman, Sungjoo Lee, William S. Marshall

Addresses: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. ' H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. ' H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. ' H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. ' H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA

Abstract: 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.

Keywords: simulation; stationary process; variance estimation; standardised time series; Cramer–von Mises estimator; batching.

DOI: 10.1504/IJSPM.2008.020608

International Journal of Simulation and Process Modelling, 2008 Vol.4 No.1, pp.1 - 6

Published online: 03 Oct 2008 *

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