Forcibly Re-scrambled Randomized Response Model for Simultaneous Estimation of Means of Two Sensitive Variables

Abstract

Recently, Ahmed et al. (Commun Stat Theory Methods 47(2):324–343, 2018) have introduced the idea of simultaneously estimating means of two sensitive variables by collecting one scrambled response and another pseudo-response. In this paper, we extend their idea to the simultaneous estimation of two means by making use of the forced quantitative randomized response model of Gjestvang and Singh (Metrika 66(2):243–257, 2007) but then re-scrambling the scrambled scores. This idea of re-scrambling already scrambled responses seems completely new in the field of randomized response sampling. The performance of the proposed forced quantitative randomized response model has been investigated analytically as well as empirically.

Keywords

Estimation of means of two sensitive characteristics / Randomized response technique / Re-scrambling / Variance and relative efficiency