Abstract

We continue our investigation into the estimation of the ratio of Binomial proportions. We concentrate on point estimation and its accuracy properties. A problem of the point estimation for a ratio of two proportions using data from two independent Bernoulli samples is considered. In this article we mostly discuss the case when the first sample is obtained using the Inverse sampling scheme and the second one using the Direct Binomial sampling scheme. Our goal is to show that the normal approximations, which are relatively simple, for estimates of the ratio are reliable for the construction of point estimators with reliable accuracy properties. The main criterion of our judgment is the bias and mean squared error. The main accuracy characteristics of estimators corresponding to all possible combinations of sampling schemes are investigated by the Monte-Carlo method. Mean values and mean squared errors of point estimators are collected in tables, and some recommendations for the application of each estimators are presented.

中文翻译：

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使用逆直接采样方案比较二项式比例的点估计器的精度属性

摘要

我们继续对二项式比例的估计进行调查。我们专注于点估计及其准确性属性。考虑了使用来自两个独立的伯努利样本的数据对两个比例的比率进行点估计的问题。在本文中，我们主要讨论使用逆采样方案获取第一个样本而使用直接二项采样方案获取第二个样本的情况。我们的目标是证明对于比率的估计而言，相对简单的正态近似对于构造具有可靠精度属性的点估计器是可靠的。我们判断的主要标准是偏差和均方误差。通过蒙特卡洛方法研究了与所有可能的采样方案组合相对应的估计量的主要准确性特征。表中收集了点估计量的平均值和均方误差，并提出了一些适用于每种估计量的建议。