Abstract

We consider a general problem of the interval estimation for a cross-product ratio \(\rho=\frac{p_{1}(1-p_{2})}{p_{2}(1-p_{1})}\) according to data from two independent samples. Each sample may be obtained in the framework of direct or inverse Binomial sampling schemes. Asymptotic confidence intervals are constructed in accordance with different types of sampling schemes, with parameter estimators demonstrating exponentially decreasing bias. Our goal is to investigate the cases when the normal approximations (which are relatively simple) for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals corresponding to all possible combinations of sampling schemes. We present estimations of the coverage probability, expectation and standard deviation of interval widths in tables and provide some recommendations for applying each obtained interval.

中文翻译：

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不同抽样方案下二项式比例的乘积比置信度估计

摘要

我们考虑交叉乘积比\（\ rho = \ frac {p_ {1}（1-p_ {2}）} {p_ {2}（1-p_ {1}）}的区间估计的一般问题\）根据来自两个独立样本的数据。每个样本都可以在直接或反向二项式抽样方案的框架中获得。渐进置信区间是根据不同类型的采样方案构造的，其中参数估计量显示出指数递减的偏差。我们的目标是研究当交叉积比的估计量的正态近似值（相对简单）对于构造置信区间可靠时的情况。我们使用置信系数与名义置信水平的接近度作为我们的主要评估标准，并使用蒙特卡洛方法研究与所有可能的采样方案组合相对应的区间的关键概率特征。我们提出了覆盖率的估计值，