Bias Properties of Budget Constrained Simulations

Peter W. Glynn and Philip Heidelberger
Additional contact information
Peter W. Glynn: Stanford University, Stanford, California
Philip Heidelberger: IBM T. J. Watson Research Center, Yorktown Heights, New York

Operations Research, 1990, vol. 38, issue 5, 801-814

Abstract: This paper addresses the bias characteristics of estimators produced from Monte Carlo simulations. If the computer time allocated to the simulation is t , then N ( t ), the number of replications completed by time t , is a renewal process. The simulation implications of a known exact expression for the expected value of a sample mean based on N ( t ) replications are explored and a similar exact expression for a sample mean based on N ( t ) + 1 replications is derived. Bias expansions for a sample mean based on N ( t ) or N ( t ) + 1 replications are obtained. The bias in the sample mean based on N ( t ) replications is at most of order o(1/ t ). Under suitable moment conditions, the bias decreases at a much faster rate than o(1/ t ); on the other hand, the estimator based on N ( t ) + 1 replications has bias of order 1/ t . The exact expressions also lead to simple and totally unbiased estimators. Using Taylor series, the bias expansions of a general function of means based on N ( t ) or N ( t ) + 1 replications are determined. The leading terms in these expansions are of order 1/ t , although the coefficients are different. Based on these expansions, a Tin-style adjusted estimator is proposed to reduce the bias. These expansions are specialized to the case of ratio estimation in regenerative simulation. Due to a cancellation effect, the ratio estimator based on N ( t ) + 1 cycles is biased only to order o(1/ t ) providing confirmation and reinterpretation of a result of M. Meketon and P. Heidelberger.

Keywords: probability: regenerative and renewal processes; simulation: statistical analysis (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.38.5.801 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:38:y:1990:i:5:p:801-814

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().