Bounds for monetary-unit sampling in auditing: an adjusted empirical likelihood approach
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Bounds for monetary-unit sampling in auditing: an adjusted empirical likelihood approach Yves G. Berger1
· Paola M. Chiodini2 · Mariangela Zenga2
Received: 6 January 2020 / Revised: 30 July 2020 © The Author(s) 2020
Abstract It is common practice for auditors to verify only a sample of recorded values to estimate the total error amount. Monetary-unit sampling is often used to over-sample large valued items which may be overstated. The aim is to compute an upper confidence bound for the total errors amount. Naïve bounds based on the central limit theorem are not suitable, because the distribution of errors are often very skewed. Auditors frequently use the Stringer bound which known to be too conservative. We propose to use weighted empirical likelihood bounds for Monetary-unit sampling. The approach proposed is different from mainstream empirical likelihood. A Monte–Carlo simulation study highlights the advantage of the proposed approach over the Stringer bound. Keywords Coverages · External audit · Nominal level · Stringer bound · Tolerable error amount · Unequal probability Sampling Mathematics Subject Classification 62D05 · 62G15 · 62G20
1 Introduction In practice, it is natural to audit only a sample of accounting records to establish the correctness of the entire financial reporting process. Audit techniques are divided into two main areas: the so-called “internal audit” which is carried out internally to monitor the accounting process, and “external audit” carried out by accounting experts who certify the correctness of the accounting recording process. We shall focus on the latter. In general, auditing aims to verify whether there are material errors in a set of N
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Yves G. Berger [email protected] http://yvesberger.co.uk
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Economic, Social and Political Sciences, University of Southampton, Southampton SO17 1BJ, UK
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Department of Statistics and Quantitative Methods, University Milano-Bicocca, Milan, Italy
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accounting records or items. The inferential problem facing the auditor is to decide, on the basis of sample information, whether the errors found on the accounting records are attributable only by random material errors or by fraudulent actions. Each item in the sample provides the auditor with two types of information: the recorded amount (or book amount) and the audited amount (or corrected amount). The difference between these two amounts is called the error which is used to estimate the overall unknown error amount. Auditors want to verify if the total error falls below a pre-assigned “tolerable error amount” denoted A hereafter. This can be achieved by calculating an upper confidence bound for the total error. If this bound is lower than A, the auditor concludes that no misstatement has been made. On the contrary, if this bound is larger than A, then the auditor may decide to verify all the recorded amounts. Alternatively, a p-value calculated at A can be used instead. The primary focus is on the upper bound of the confidence interval rather than point estim
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