An Improved Two-Stage Randomized Response Model for Estimating the Mean of a Quantitative Sensitive Random Variable

Document Type : Original Article

Authors
Rawan Arafa
Reda Mazloum
Statistics Department, Faculty of Economics and Political Science, Cairo University, Egypt.
10.22034/jirss.2022.707639
Abstract
This paper introduces a new two-stage randomized response model for estimating the mean of a sensitive quantitative random variable. The proposed model is obtained for both simple and stratified random sampling. The efficiency of the proposed estimator, under both sampling schemes, is investigated with respect to various estimators and it is found to be more efficient. Moreover, a new measure for evaluating the performance of any randomized response estimator is introduced. The measure considers the relative efficiency of the randomized response estimator, and the privacy protection it offers. The performance of the proposed estimator is examined using the new measure and it is found to have an overall better performance than its rival estimators. A real data example is also examined using the proposed model and various models from literature.
Keywords
Efficiency
Privacy Protection
Scrambling Variable
Simple Random Sampling
Stratified Random Sampling
Subjects
Bar-Lev, S. K., Bobovitch, E., and Benzion, B. (2004), A note on randomized response models for quantitative data, Metrika, 60(3), 255-260.
Diana, G. and Perri, P. F. (2011), A class of estimators for quantitative sensitive data, Statistical Papers, 52, 633-650.
Eichhorn, B. H., and Lakhbir S. Hayre, L. S. (1983), Scrambled randomized response methods for obtaining sensitive quantitative data, Journal of Statistical Planning and Inference, 7(4), 307 - 316.
Greenberg, B. G, Kuebler Jr, R. R, Abernathy,J. R., and Horvitz, D. G. (1971), Application of the Randomized Response Technique in Obtaining Quantitative Data, Journal of the American Statistical Association, 66(334), 243-250.
Gupta, S., Gupta , B. and Singh, S. (2002), Estimation of sensitivity level of personal interview survey questions,Journal of Statistical Planning and Inference, 100(2), 239-247.
Odumade, O. and Singh, S. (2009), Improved Bar-Lev, Bobovitch, and Boukai Randomized Response Models,Communications in Statistics - Simulation and Computation, 38(3), 473-502.
Ryu, J. B., Kim, J. M., Heo, T. Y., and Park, C. G. (2005), On stratified randomized response sampling, Model Assisted Statistics and Applications, 1(1), 31-36.
Singh, H. P. and Gorey, S. (2019), A modified efficient randomized response model,Investigacion Operacional, 40(3), 374-385.
Warner, S. L. (1965), Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias, Journal of the American Statistical Association, 60(309), 63-69.
Journal of the Iranian Statistical Society
Volume 21, Issue 2
December 2022
Pages 89-110

  • Receive Date 09 April 2022
  • Revise Date 28 June 2023
  • Accept Date 15 September 2023