Optional randomized response techniques for quantitative characteristics

Abstract

Gupta et al. and Huang considered optional randomized response techniques where the probability of choosing the randomized (or direct) response is fixed for all the respondents. In this paper the assumption of the constant probability of choosing the option has been relaxed by dividing respondents into two groups: one group provides direct response and the second a randomized response. The method of estimation of the population mean and variances under the modified assumption are obtained. Relative efficiencies of the proposed techniques are compared theoretically and empirically.

Keywords:

• Randomized response
• relative efficiency
• sampling scheme

Acknowledgments

The author is grateful to the referees for their valuable suggestions that lead to improvement of the final manuscript. The author also wishes to thank Prof. N. Greaves for editing the manuscript.