Chaudhuri and Mukerjee ORRT for two sensitive characteristics and their overlap

Abstract

In this paper, we extend the optional randomized response technique (ORRT) developed by Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988] to the situation of estimating the proportion of two sensitive characteristics and their overlap. Lee, Sedory and Singh [Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. Stat Prob Lett. 2013;83(1):399–409; Estimation of odds ratio, attributable risk, relative risk, correlation coefficient and other parameters using randomized response techniques. Behaviormetrika. 2021;48:371–392.] have shown that their crossed model performs better than their simple model from an efficiency point of views. Here we investigated a further improvement in the crossed model along the lines of Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988]. New unbiased estimators are proposed, their variance expressions are derived and estimators of variances are suggested. Lastly, we carry out a simulation study to investigate the behaviour of the proposed estimators with respect to their competitors.

KEYWORDS:

• Sensitive characteristics
• randomized response sampling
• relative efficiency
• protection of respondents

Acknowledgements

The authors are grateful to the Editor Dr. Richard G. Krutchkoff, an Associate Editor and two referees for their valuable comments on the original version of the manuscript. The authors are also grateful to Prof. Stephen Sedory for four-week long discussions during the revision and also for its editing.

Disclosure statement

No potential conflict of interest was reported by the author(s).