Abstract

In this article, we investigate the confidence estimation of the ratio of Binomial proportions. Contrary to the previous research, where independent Bernoulli samples were considered, here we concentrate on the confidence estimation of dependent (correlated) samples. We use data from two dependent samples to explore general problem of the estimating a ratio of two proportions. Each sample is obtained in the framework of direct binomial sampling. Our goal is to show that the normal approximation (which is relatively simple) for estimates of the ratio are reliable for the construction of confidence estimators. The main criterion of our judgment is the coverage probability and the width of the corresponding confidence interval. The main characteristics of confidence estimators are investigated by the Monte-Carlo method. Coverage probability and width of the confidence intervals are collected in tables, and some recommendations for an application are presented.

中文翻译：

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相依人口二项比例的置信度估计

摘要

在本文中，我们研究了二项式比例的置信度估计。与先前的研究（其中考虑了独立的伯努利样本）相反，这里我们专注于相关（相关）样本的置信度估计。我们使用来自两个相关样本的数据来探索估计两个比例之比的一般问题。每个样本都是在直接二项式抽样的框架中获得的。我们的目标是证明对比率的估计的正态逼近（相对简单）对于构造置信估计量是可靠的。我们判断的主要标准是覆盖概率和相应置信区间的宽度。通过蒙特卡洛方法研究置信估计量的主要特征。