An improved randomized response model: estimation of mean

Abstract

In this paper, we suggest a new randomized response model useful for collecting information on quantitative sensitive variables such as drug use and income. The resultant estimator has been found to be better than the usual additive randomized response model. An interesting feature of the proposed model is that it is free from the known parameters of the scrambling variable unlike the additive model due to Himmelfarb and Edgell [S. Himmelfarb and S.E. Edgell, Additive constant model: a randomized response technique for eliminating evasiveness to quantitative response questions, Psychol. Bull. 87(1980), 525–530]. Relative efficiency of the proposed model has also been studied with the corresponding competitors. At the end, an application of the proposed model has been discussed.

Keywords:

• sensitive variable
• estimation of mean
• randomized response model
• scrambling variables

Acknowledgements

The authors are thankful to the Editor Robert G. Aykroyd and two learned referees for the constructive comments on the original version of the manuscript. Thanks are also due to Professor David H. Robinson, Chair, Department of Statistics and Computer Networking, for help in completing this paper. The help from a professional English Editor Ms Melissa Lindsay, Writing Place Center, St Cloud State University, for editing the entire manuscript has been duly acknowledged.