Improving the accuracy of total estimates for complex sampling in auditing

In the practice of auditing, for cost concerns, auditors verify only a sample of accounts to estimate the error of the total population of accounts. Common statistical methods to select an audit sample are by without replacement or by probability proportional to size (PPS). A particular case of the PPS is the monetary unit sampling (MUS) (Arens and Loebbecke, 1981), that is popular because it directs efforts towards high-valued items which contain the greatest potential of large overstatement. Frequently the auditors apply this method without any theoretical support for the accuracy of the total estimates for the audit situation. In an accounting population consisting of N line items with book (or recorded)values, x1,x2,…,xN and T_x=∑_(i=1)^N▒x_i is the total book amount. The errors are denoted by y1,y2,…,yN so that xi-yi are the true or audited values. A sample of line items is chosen and audited in order to estimate the total error amount T_y=∑_(i=1)^N▒y_i . The book values are considered as realizations of an auxiliary variable, which is generally skewed. In literature the upper confidence limit for Ty is considered to evaluate the performance of the sampling method. Since estimators of Ty based on large-sample normal distribution theory have been found to have a coverage much less than the stated confidence level (Kaplan, 1973; Neter and Loebbecke, 1975 and Beck 1980), auditors frequently use heuristic non-classical bound estimates to determine the accuracy of financial statements (Horgan, 1996). The aim of this work is to apply the empirical likelihood technique for estimation of upper bound of total error amount as proposed by Berger and De La Riva Torres in 2012 using even simulation data and real data set (obtained by an auditing company). The proposed approach based on the empirical likelihood technique gives design-based confidence intervals which may have better coverages than standard confidence intervals, pseudo empirical likelihood and bootstrap confidence intervals.