A composite class of estimators using scrambled response mechanism for sensitive population mean in successive sampling

ABSTRACT

This paper considers the problem of estimation of population mean of a sensitive characteristics using non-sensitive auxiliary variable at current move in two move successive sampling. The proposed estimator is studied under five different scrambled response models. Various estimators have been elaborated to be the member of the proposed class of estimators. The properties of the proposed estimators have been analysed. Many estimators belonging to the proposed class have been explored under five scrambled response models. In order to identify the scrambled model effect, the proposed composite class of estimators is compared to the direct methods. Respondents privacy protection have also been elaborated under different models. Theoretical results are supplemented with numerical demonstrations using real data. Simulation has been carried out to show the applicability of proposed estimators and hence suitable recommendations are forwarded.

Keywords:

• Bias
• Class of estimators
• Mean squared error
• Optimum matching fraction
• Population mean
• Scrambled response model
• Sensitive variable
• Successive moves

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgments

Authors are thankful to the anonymous reviewers for their valuable and inspiring suggestions, which lead to improvement over an earlier version of the paper. Authors are also thankful to SERB, New Delhi, India for providing the financial assistance to carry out the present work. Authors acknowledged the free access to data by statistical abstracts of United states.

Additional information

Funding

Science and Engineering Research Board. EMR/2016/000455.