Application of the ECM algorithm to the estimation of the likelihood function in financial auditing

• Published in: Scientific Papers of Silesian University of Technology Organization and Management Series Vol. 2024; no. 198; pp. 475 - 487
• Main Author: Sitek, Grzegorz
• Format: Journal Article
• Language: English
• Published: 2024
• ISSN: 1641-3466
• DOI: 10.29119/1641-3466.2024.198.26

Purpose: The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non-zero errors amounts. Below we consider a problem of testing appropriately formulated statistical hypotheses about admissibility of the total or the mean accounting errors. Hypotheses can be verified by the likelihood ratio test. In this paper, we show how to estimate parameters of the likelihood function. Design/methodology/approach: The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non- zero errors amounts. Below we consider a problem of testing appropriately formulated statistical hypotheses about admissibility of the total or the mean accounting errors. Hypotheses can be verified by the likelihood ratio test. In this paper, we show how to estimate parameters of the likelihood function. Findings: The work presents formulas for the parameters of the likelihood function. These parameters were obtained using the ECM algorithm. Originality/value: The problem of estimating the average audit error is very common in economic research. A method for estimating the average audit error based on the likelihood function was proposed. The parameters of the likelihood function were estimated using the ECM algorithm. Keywords: ECM algorithm, likelihood ratio test, mixture of probability distribution. Category of the paper: Research paper.