有界随机变量的检验鞅
Test Martingales for bounded random variables
摘要：
给定来自随机变量$T$的随机样本，该随机变量从上有界，$T\leτ$ a.s.，我们定义过程是正上鞅，如果$E(T)\geμ$。这类过程称为测试鞅。上鞅假设的检验隐含地检验了假设$H_0:E(T)\geμ$。我们构造的测试鞅，导致测试与权力1。我们还构造了置信度上界。我们扩展的技术测试$H_0:E(T)=μ$和构造置信区间。在财务审计中，随机抽样被建议作为一种可能的技术，以收集足够的保证，能够说明财务报告中没有“重大”错报。我们的工作目标是提供一个数学背景，可以代表这样的过程中收集保证通过重复随机抽样。
英文摘要：
Given a random sample from a random variable $T$ which is bounded from above, $T\leτ$ a.s., we define processes that are positive supermartingales if $E(T)\geμ$. Such processes are called test martingales. Tests of the supermartingale hypothesis implicitly test the hypothesis $H_0:E(T)\geμ$. We construct test martingales that lead to tests with power 1. We also construct confidence upper bounds. We extend the techniques to testing $H_0:E(T)=μ$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
