Department of Mathematics, COMSATS University Islamabad, Wah Campus, Pakistan.
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, USA.
Biom J. 2021 Jan;63(1):134-147. doi: 10.1002/bimj.201900137. Epub 2020 Oct 25.
In this paper, we develop a new methodology that indicates that the use of correlated scrambling variables in the randomized response technique may play an important role in increasing the efficiency of an estimator of the population mean of a sensitive variable. Although it is clear analytically that the proposed estimator is more efficient than its existing competitors, we have investigated the magnitude of the gain in efficiency through simulation studies that involve both real secondary data from the health sciences, as well as artificial data. We also derive an estimator of the variance of the proposed estimator of mean and we study the coverage of 95% confidence intervals based on this variance estimator. An application using real primary data on smoking by university students is also included.
在本文中，我们提出了一种新方法，表明在随机响应技术中使用相关的混淆变量可以在提高敏感变量总体均值估计量的效率方面发挥重要作用。虽然从理论上可以清楚地看出，所提出的估计量比现有的竞争对手更有效，但我们通过涉及健康科学领域的真实二次数据和人工数据的模拟研究，研究了效率提高的幅度。我们还推导出了一种均值估计量的方差估计量，并研究了基于该方差估计量的 95%置信区间的覆盖情况。还包括了一个使用大学生吸烟的真实原始数据的应用。
