A Unified Approach for Analysis of Randomized Response Surveys
In this paper, we propose a class of estimators for the population mean of a sensitive variable, taking account into a generic randomization scheme, under the simple random sampling with replacement (SRSWR), 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 defined. We prove that the best estimator acts as a regression estimator which is at least as efficient as the corresponding estimator without the auxiliary variable. A new measure of privacy protection is built, and some models can be compared from the perspective of efficiency and privacy protection.
H. Wang, B.J. Zhang, X.Z. Liu, D.Z. Luo, S.B. Zhong
Z. M. Hong and Z. Z. Yan, "A Unified Approach for Analysis of Randomized Response Surveys", Advanced Materials Research, Vols. 143-144, pp. 1259-1263, 2011