A Combined Bound for Errors in Auditing Based on Hoeffding's Inequality and the Bootstrap

Abstract

For an accounting population's total error amount, confidence bounds that are reliable but not too conservative help auditors avoid costly overauditing. Parametric methods that have been proposed are not always robust. To date, none of the nonparametric methods proposed have shown superiority over the others in all population settings. This article describes a simulation study of a nonparametric bound on the total error amount in an auditing population when dollar-unit sampling is employed. The bound is a combination of two new bounds, one generated by Hoeffding's inequality and the other by a modified nonparametric bootstrap-t method that makes use of today's powerful yet cheap and readily available computer technology. At the 95% confidence level for sample size 120, the combined bound is reliable over a wide range of simulated study populations and is on average 13% smaller than the benchmark Stringer bound based on the binomial distribution. For real accounting populations, the combined bound remains reliable and is on average 24% smaller than the Stringer bound.

KEY WORDS:

• Dollar-unit sampling
• Monte Carlo
• Nonstandard mixture
• Skewed distribution