2021/09/18 by Harrie Hendriks, Hendriks, Harrie
Decision Sciences · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Probability and Risk Models #Risk and Portfolio Optimization #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.2109.08923
This revision of arXiv:1801.09418 contains more precise statements about the expected run time of the tests. It also contains references to recent relevant publications
arxiv created 2021/09/18 · openalex publication_date 2021/09/18 · arxiv updated 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a positive random variable X, X≥0 a.s., a null hypothesis H0:E(X)≤μ and a random sample of infinite size of X, we construct test supermartingales for H0, i.e. positive processes that are supermartingale if the null hypothesis is satisfied. We test hypothesis H0 by testing the supermartingale hypothesis on a test supermartingale. We construct test supermartingales that lead to tests with power 1. We derive confidence lower bounds. For bounded random variables we extend the techniques to two-sided tests of H0:E(X)=μ and to the construction of confidence intervals. In financial auditing random sampling is proposed as one of the possible techniques to gather enough evidence to justify rejection of the null hypothesis that there is a 'material' misstatement in a financial report. The goal of our work is to provide a mathematical context that could represent such process of gathering evidence by means of repeated random sampling, while ensuring an intended significance level.