This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables $X_1,\ldots, X_{n}$ are observed, we have proposed randomized tests with a randomization parameter for the upper confidence limit of the expectation of the $(n+1)$th random variable $X_{n+1}$ under a given significance level $\delta>0$. Our proposed randomized test significantly improves over deterministic test unlike random sampling with replacement.
翻译:本文在随机抽样中研究单方假设测试而无需替换。 也就是说, 当美元+1美元( 美元+1美元)的二进制随机变量 $X_ 1,\ldots, X ⁇ n+1} 美元时, 当美元+1美元( 美元+1美元)的随机随机变量 $X_ 1,\\\ldots, X ⁇ n} 美元时, 我们观察到了美元+1, 美元+1的随机随机变量 $x_ 1, 也就是当美元+1美元( 美元+1美元) 时, 我们建议随机测试与随机抽样替换不同, 随机测试比确定性测试大有改进。