Inference and Auditing: The Stringer Bound

Abstract

Summary Accounting practice calls for nonparametric upper confidence bounds on the total error amount in accounting populations. Dollar unit sampling and the assumption that actual value never exceeds book value lead to the problem of setting a nonparametric upper confidence bound on the mean of a population taking values between 0 and 1 on the basis of a sample from that population. The usual Gaussian asymptotic theory bounds are unsatisfactory since, though samples are large, there are few informative (nonzero) observations. An ad hoc bound, the so called Stringer bound, has been found to be conservative and is widely used in accounting practice but its theoretical properties are essentially unknown. We give some weak fixed sample support to the bound's conservativeness and show that asymptotically it is essentially always too big. In addition we discuss a number of bounds which can be shown to be conservative and propose a simple new procedure which, initial simulations suggest, shares the conservatism of the Stringer bound for small numbers of nonzero observations and behaves like the asymptotically correct Gaussian based bound for larger numbers of nonzero observations.