1. On the Warnock-Halton quasi-standard error.
- Author
-
Owen, Art B.
- Subjects
MONTE Carlo method ,ESTIMATION theory ,ERROR analysis in mathematics ,MATHEMATICAL statistics ,NUMERICAL analysis - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2006
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