We derive and examine the interval width and coverage properties of an integrated-likelihood-ratio confidence interval for the binomial parameter p using a double-sampling scheme. The data consist of a relatively large fallible sample containing underreported data and a relatively small infallible subsample. Via Monte Carlo simulations, we determine that the new integrated-likelihood-ratio interval estimator displays slightly conservative to moderately conservative coverage properties for small to medium sample sizes and can have shorter average-interval width than two previously proposed confidence intervals when p < 0.10 or p > 0.90. We also apply the integrated-likelihood-ratio confidence interval to a real-data set and determine that the integrated-likelihood-ratio interval has superior performance when contrasted to two properties of two competing confidence intervals.

中文翻译：

---

基于漏报和可靠数据的比例的综合似然比置信区间

我们使用双采样方案推导出并检查二项式参数p的积分似然比置信区间的区间宽度和覆盖率属性。数据由包含漏报数据的相对较大的易错样本和相对较小的易错子样本组成。通过蒙特卡洛模拟，我们确定新的综合似然比区间估计器对于中小样本规模显示出略微保守到适度保守的覆盖属性，并且当p  < 0.10 或p < 0.10时，平均区间宽度可以比之前提出的两个置信区间更短。磷 > 0.90。我们还将集成似然比置信区间应用于实际数据集，并确定与两个竞争置信区间的两个属性相比，集成似然比区间具有更好的性能。