On the dispersion matrix of variance estimators of the sample mean in the analysis of simulation output

  • Authors:
  • Wheyming Tina Song;Bruce Schmeiser

  • Affiliations:
  • School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA;School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1988

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Abstract

A classical problem of stochastic simulation is how to estimate the variance of point estimators, the prototype problem being the sample mean from a steady-state autocorrelated process. A variety of estimators for the variance of the sample mean have been proposed, all designed to provide robustness to violations of assumptions, small variance, and reasonable computing requirements. Evaluation and comparison of such estimators depend on the ability to calculate their variances. A numerical approach is developed here to calculate the dispersion matrix of a set of estimators expressible as quadratic forms of the data. The approach separates the analysis of the estimator type from the analysis of the data type. The analysis for overlapping-batch-means estimators is developed, as is the analysis for steady-state first-order autoregressive and moving-average data. Closed-form expressions for overlapping-batch-means estimators and independently distributed data are obtained.