A General Model for Repeated Audit Controls Using Monotone Subsampling

In categorical repeated audit controls, fallible auditors classify sample elements in order to estimate the population fraction of elements in certain categories.To take possible misclassifications into account, subsequent checks are performed with a decreasing number of observations.In this paper a model is presented for a general repeated audit control system, where k subsequent auditors classify elements into r categories.Two different sub-sampling procedures will be discussed, named 'stratified' and 'random' sampling.Although these two sampling methods lead to different probability distributions, it is shown, based on sufficiency, that the likelihood inferences are identical.The MLE and accompanying limit distributions are derived.The situations with undefined MLE are examined in detail; it is shown that an unbiased MLE can be acquired by stratified sampling.