We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper–Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.

中文翻译：

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使用排序集抽样的比例的可靠置信区间

我们开发了两种新的近似置信区间方法，用于使用平衡排名集抽样（RSS）估计人口比例。与现有的基于RSS的方法不同，新方法不仅在完美排名下而且在不完美排名下也能很好地控制覆盖率。一种方法使用威尔逊型间隔，另一种方法基于对Clopper–Pearson型间隔进行中P调整。当给出总比例时，这两种方法都依赖于新的基于最大似然法的方法来估计判断层中的比例，并且即使对于大样本量也可以计算两者。