On the Warnock-Halton quasi-standard error

Owen Art B. ()
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Owen Art B.: E-mail: owen@stanford.edu

Monte Carlo Methods and Applications, 2006, vol. 12, issue 1, 47-54

Abstract: This paper investigates an error estimate proposed by Warnock and studied by Halton (2005). That error estimate is simply the sample standard error applied to certain non-randomized quasi-Monte Carlo points. This quasi-standard error (QSE) closely tracks the actual error in an example, and looks to be at least as accurate as a standard error based on random replication. We also show that the quasi-standard error is not unreasonably large in its intended use. But there are quasi-Monte Carlo (QMC) constructions for which the QSE severely underestimates the true error. Moreover, discrepancy considerations do not separate these counter-examples from other cases where the method might be reliable. We conclude that the QSE is not yet ready to be trusted in applications.

Date: 2006
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DOI: 10.1515/156939606776886652

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