2018/01/29 by Harrie Hendriks, Hendriks, Harrie · 2 citations
Decision Sciences · Mathematics · #62L12 #FOS: Computer and information sciences #Methodology (stat.ME) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #msc:62L12 #stat.ME
paper · pdf · doi:10.48550/arxiv.1801.09418
openalex publication_date 2018/01/29 · arxiv created 2018/02/18 · arxiv updated 2018/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a random sample from a random variable T which is bounded from above, T≤τ a.s., we define processes that are positive supermartingales if E(T)≥μ. Such processes are called test martingales. Tests of the supermartingale hypothesis implicitly test the hypothesis H0:E(T)≥μ. We construct test martingales that lead to tests with power 1. We also construct confidence upper bounds. We extend the techniques to testing H0:E(T)=μ and constructing confidence intervals. In financial auditing random sampling is proposed as one of the possible techniques to gather enough assurance to be able to state that there is no 'material' misstatement in a financial report. The goal of our work is to provide a mathematical context that could represent such process of gathering assurance by means of repeated random sampling.