Asymptotic Validity of Batch Means Steady-State Confidence Intervals

Peter W. Glynn () and Eunji Lim ()
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Peter W. Glynn: Stanford University
Eunji Lim: University of Miami

A chapter in Advancing the Frontiers of Simulation, 2009, pp 87-104 from Springer

Abstract: Abstract The method of batch means is a widely applied procedure for constructing steady-state confidence intervals. The traditional theoretical support for the method of batch means has rested on the assumption of a functional central limit theorem for the underlying process. We establish here that the method of batch means is valid for Harris recurrent Markov processes whenever the associated process satisfies a simple (non–functional) central limit theorem. This weaker condition for validity of the method of batch means is also shown to hold in the setting of one-dependent regenerative processes.

Keywords: Markov Process; Central Limit Theorem; Stationary Stochastic Process; Functional Central Limit Theorem; Cancellation Method (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-0817-9_5

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DOI: 10.1007/b110059_5

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