An innovative optimal randomized response model using correlated scrambling variables

Abstract

This paper introduces an innovative and optimal randomized response model by making use of correlated scrambling variables for estimating the population mean of a sensitive variable. The resultant estimators are found to be unbiased. Variance expressions of the proposed estimators have also been derived. Analytical as well as empirical evidences are provided in favour of the proposed estimators relative to their competitors. A possible extension to a general method is also suggested.

Keywords:

• Optimum estimation
• population mean
• sensitive variable
• correlated scrambling variables
• scrambled response

Acknowledgments

The authors are thankful to the Editor Professor Richard G. Krutchkoff, an Associate Editor and a learned referee to bring the original manuscript in the present form. The authors are also thankful to Professor Dr. Stephen A. Sedory, Department of Mathematics, Texas A & M University-Kingsville, for editing the revised manuscript. It is worth mentioning that the current study is based on research work carried out by the lead author Maryam Murtaza as partial requirement of doctoral degree that she is currently pursuing from Quaid-i-Azam University, Islamabad, Pakistan. We also acknowledge the R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

Disclosure statement

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