New scrambled response models for estimating the mean of a sensitive quantitative character

Abstract

Moving from the scrambling mechanism recently suggested by Saha [25], three scrambled randomized response (SRR) models are introduced with the intent to realize a right trade-off between efficiency and privacy protection. The models perturb the true response on the sensitive variable by resorting to the multiplicative and additive approaches in different ways. Some analytical and numerical comparisons of efficiency are performed to set up the conditions under which improvements upon Saha's model can be obtained and to quantify the efficiency gain. The use of auxiliary information is also discussed in a class of estimators for the sensitive mean under a generic randomization scheme. The class includes also the three proposed SRR models. Finally, some graphical comparisons are carried out from the double perspective of the accuracy in the estimates and respondents’ privacy protection.

Keywords:

• auxiliary variable
• class of estimators
• privacy protection
• sensitive variable

Acknowledgments

The authors wish to thank two anonymous referees for their careful reading and constructive suggestions which led to improvement over an earlier version of the paper. Work supported by the Italian Ministry of University and Research, MIUR-PRIN 2007: “Efficient use of auxiliary information at the design and at the estimation stage of complex surveys: methodological aspects and applications for producing official statistics”.