Some alternative additive randomized response models for estimation of population mean of quantitative sensitive variable in the presence of scramble variable

Abstract

This article addresses the estimation procedures of population mean related to the quantitative sensitive variable with the help of a randomized device which makes the use of blank cards in the randomization process. Two different randomized techniques are proposed which consisting the special models for each device. The proposed techniques provide the unbiased estimation procedures of population mean along with enhanced privacy protection of the respondents. The comparisons of the resultant estimators have been made with respect to the Perri (2008) estimator. Numerical illustrations are presented to support the theoretical results and suitable recommendations are put forward to the survey statisticians.

Keywords:

• Blank card procedure; Additive models; Privacy; Quantitative variable; Unrelated question models

Mathematics Subject Classification:

• 62D05

Acknowledgments

The authors are grateful to the learned referee for bringing the original manuscript to its present form. Authors are also thankful to the IIT(ISM), Dhanbad for providing the financial assistance and necessary infrastructure to carry out the present work.