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.

中文翻译：

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相关加扰变量在定量随机响应技术中的使用

在本文中，我们开发了一种新方法，表明在随机响应技术中使用相关加扰变量可能在提高敏感变量总体均值估计器的效率方面发挥重要作用。尽管在分析上很明显，提议的估计器比其现有的竞争对手更有效，但我们已经通过模拟研究调查了效率提高的幅度，这些模拟研究涉及来自健康科学的真实二手数据以及人工数据。我们还推导出了建议的均值估计量的方差估计量，并基于该方差估计量研究了 95% 置信区间的覆盖范围。还包括使用大学生吸烟的真实原始数据的应用程序。