Privacy protection measures for randomized response surveys on stigmatizing continuous variables

We consider the situation where sample surveys are to be undertaken on sensitive or stigmatizing issues. For such surveys, direct questioning methods usually lead to non-compliance or incorrect responses and so, the randomized response technique, where the responses are collected through some randomization device, is found to be useful. A majority of the literature on these techniques focus on dichotomous sensitive variables, while some techniques are also available for continuous sensitive variables. In this article, we focus on the extent of privacy protection available in sample surveys to respondents for continuous response variables. We also propose two measures of privacy protection. We demonstrate that the parameters of our randomization scheme can be so chosen as to achieve a pre-assigned level of privacy protection while at the same time yielding efficient estimates. We also show some numerical comparisons.