Respondent privacy and estimation efficiency in randomized response surveys for discrete-valued sensitive variables

Abstract

In some socio-economic surveys, data are collected on sensitive issues such as tax evasion, criminal conviction, drug use, etc. In such surveys, direct questioning of respondents is not of much use and the randomized response technique is used instead. A few researchers have studied the issue of privacy protection for surveys where the objective is to estimate the proportion of persons bearing the sensitive trait. Not much is known about respondent protection when the variable under study is a discrete quantitative variable and the objective is to estimate the population mean. In this article we study this issue. We propose a scheme for this issue and a measure of privacy. We show that given a stipulated level of this privacy measure, we can determine the parameter of the randomization device so as to maximize the efficiency of estimation, while guaranteeing the desired level of privacy protection.