Introduction: In biometric sample surveys, our objective is to get ready-made information for future planning and policy implementations related to the subject matters of highly sensitive issues. In such situations, we apply randomized response/scrambled response techniques. There are many highly sensitive issues which need to be examined over time as they may have a tendency to change. To get rid of these types of practical cases we need a scrambled response technique on successive occasions. Methods: Using an additive and multiplicative technique, we proposed new effective scrambled response models to estimate the population mean of quantitative sensitive char-acteristics. Degree of privacy protection and unified measure approaches are used to examine the efficacy of the proposed models. Efficiency of the proposed models has been checked using MATLAB software. The utility of the proposed models under two occasions of successive sampling has been also explored using exponential-type estimators. Empirical and simulation studies are carried out to justify the proposition of the proposed estimators using MATLAB software. Results: The percent relative efficiencies of the proposed models are always greater than 100 with respect to the well-known Bar-Lev et al model. In terms of degree of privacy protection, most of the values are greater than 0.5 and closer to 1. Similarly, the values of the proposed models are smaller with respect to the Bar-Lev et al model in terms of a unified measure approach. When the proposed scrambled response models are used on successive occasions, the percent relative efficiency is always found greater than 100 for all cases over its competitors. Discussion: In this study, after deeply examining the properties of the proposed models, we found that the proposed models performed better over the well-known existing model. The proposed models may be used in human survey when we deal with highly sensitive issues. The proposed models also performed better when we utilized them in successive sampling. Hence, if sensitive characteristics change with time, the proposed estimators may be the best alternative to deal with these types of situations. Mathematics Subject Classification: 62D05.
Bibliographical noteFunding Information:
The authors are thankful to the Indian Institute of Technology (Indian School of Mines), Dhanbad and College of Science and Theoretical Studies, Saudi Electronic University, KSA for providing financial and necessary infrastructural support to carry out the present research work. Authors are also thankful to the honorable reviewers, honorable editor and honorable editorial board for their valuable suggestions which improved the quality of the manuscript.
© 2021 Singh et al.
- Mean square error
- Monte Carlo simulation
- Privacy protection
- Scrambled response model
- Successive sampling