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On the Warnock-Halton quasi-standard error

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  • Owen Art B.

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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.

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  • Owen Art B., 2006. "On the Warnock-Halton quasi-standard error," Monte Carlo Methods and Applications, De Gruyter, vol. 12(1), pages 47-54, March.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:1:p:47-54:n:3
    DOI: 10.1515/156939606776886652
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    1. Snyder, William C, 2000. "Accuracy estimation for quasi-Monte Carlo simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 131-143.
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