On the Warnock-Halton quasi-standard error

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. © VSP 2006.