Mean and sensitivity estimation of a sensitive variable through additive scrambling

Abstract

This article focuses on reducing the additional variance due to randomization of the responses. The idea of additive scrambling and its inverse has been used along with (i) split sample approach and (ii) double response approach. Specifically, our proposal is based on Gupta et al. (2006) randomized response model. We selected this model for improvement because it provides estimator of mean and sensitivity level of a sensitive variable and is better than all of its competitors proposed earlier to it and even Gupta et al. (2006) sensitivity estimator is better than that of Gupta et al. (2010). Our suggested estimators are unbiased estimators and perform better than Gupta et al. (2006) estimator. The issue of privacy protection is also discussed.

Keywords:

• Additive and subtractive scrambling
• Dependent estimators and privacy protection
• Randomized response models
• Sensitive surveys

Mathematics Subject Classification:

• 62D05

Funding

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (130-078-D1433). The authors, therefore, acknowledge with thanks DSR technical and financial support.