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Estimating a sensitive proportion through randomized response procedures based on auxiliary information

机译:通过基于辅助信息的随机响应程序估算敏感比例

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Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner's (J Am Stat Assoc 60:63-69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent's privacy protection and to better estimate the proportion of people, pi (A) , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai's (Model Assist Stat Appl 1:125-130, 2006) recent work, in this paper we provide a class of estimators for pi (A) , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons' model.
机译:随机应答技术广泛用于处理敏感问题的调查中,以确保受访者的匿名性,并减少无应答者的比率和偏见。自从华纳(J Am Stat Assoc 60:63-69,1965)的开创性工作以来,已经提出了许多巧妙的装置来增强受访者的隐私保护并更好地估计具有敏感属性的人pi(A)的比例。尽管在估计非敏感参数时大量使用了辅助信息,但是当辅助变量可用时,很少进行改善随机化策略性能的尝试。从Zaizai(2006年Assist Stat Appl 1:125-130模型)的最新工作转移而来,在本文中,当补充非敏感变量的均值时,对于通用随机方案,我们为pi(A)提供了一类估计量是众所周知的。获得该类别的最小可达到方差界限,并确定最佳估计量。我们证明了最佳估计量充当回归型估计量,其效率至少与不考虑辅助变量的情况下所估计的相应估计量一样有效。然后将一般结果应用于Warner和Simmons的模型。

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