An efficient application of scrambled response approach to estimate the population mean of the sensitive variables
DOI:
https://doi.org/10.53391/mmnsa.2022.011Keywords:
Randomized response technique, simple random sampling, scrambling response, sensitive and non-sensitive variables, exponential-type estimatorsAbstract
In the presence of one auxiliary variable and two auxiliary variables, we analyze various exponential estimators. The ranks of the auxiliary variables are also connected with the study variables, and there is a linkage between the study variables and the auxiliary variables. These ranks can be used to improve an estimator's accuracy. The Optional Randomized Response Technique (ORRT) and the Quantitative Randomized Response Technique are two techniques we utilize to estimate the sensitive variables from the population mean (QRRT). We used the scrambled response technique and checked the proposed estimators up to the first-order of approximation. The mean square error (MSE) equations are obtained for all the proposed ratio exponential estimators and show that our proposed exponential type estimator is more efficient than ratio estimators. The expression of mean square error is obtained up to the first degree of approximation. The empirical and theoretical comparison of the proposed estimators with existing estimators is also be carried out. We have shown that the proposed optional randomized response technique and quantitative randomized response model are always better than existing estimators. The simulation study is also carried out to determine the performance of the estimators. Few real-life data sets are also be applied in support of proposed estimators. It is observed that our suggested estimator is more efficient as compared to an existing estimator.
Downloads
References
Gupta, S., Gupta, B., & Singh, S. Estimation of sensitivity level of personal interview survey questions. Journal of Statistical Planning and Inference, 100(2), 239-247, (2002).
Haq, A., & Shabbir, J. Improved family of ratio estimators in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 42(5), 782-799, (2013).
Warner, S.L. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309), 63-69, (1965).
Laplace, P.S. A philosophical essay on probabilities, 1819. English translation, Dover, (1951).
Sousa, R., Shabbir, J., Corte Real, P., & Gupta, S. Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information. Journal of Statistical Theory and Practice, 4(3), 495-507, (2010).
Gupta, S., Kalucha, G., Shabbir, J., & Dass, B.K. Estimation of finite population mean using optional RRT models in the presence of nonsensitive auxiliary information. American Journal of Mathematical and Management Sciences, 33(2), 147-159, (2014).
Noor-Ul-Amin, M., Mushtaq, N., & Hanif, M. Estimation of mean using generalized optional scrambled responses in the presence of non-sensitive auxiliary variable. Journal of Statistics and Management Systems, 21(2), 287-304, (2018).
Waseem, Z., Khan, H., & Shabbir, J. Generalized exponential type estimator for the mean of sensitive variable in the presence of non-sensitive auxiliary variable. Communications in Statistics-Theory and Methods, 50(14), 3477-3488, (2021).
Gupta, S., Shabbir, J., & Sehra, S. Mean and sensitivity estimation in optional randomized response models. Journal of Statistical Planning and Inference, 140(10), 2870-2874, (2010).
Grover, L.K., & Kaur, P. An improved estimator of the finite population mean in simple random sampling. Model Assisted Statistics and Applications, 6(1), 47-55, (2011).
Grover, L.K., & Kaur, P. A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable. Communications in Statistics-Simulation and Computation, 43(7), 1552-1574, (2014).
Platt, W.J., Evans, G.W., & Rathbun, S.L. The population dynamics of a long-lived conifer (Pinus palustris). The American Naturalist, 131(4), 491-525, (1988).
Waseem, Z., Khan, H., Shabbir, J., & Fatima, S.E. A generalized class of exponential type estimators for estimating the mean of the sensitive variable when using optional randomized response model. Communications in Statistics-Simulation and Computation, 1-13, (2020).
Eichhorn, B.H., & Hayre, L.S. Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistical Planning and inference, 7(4), 307-316, (1983).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Atiqa Zahid, Saadia Masood, Sumaira Mubarik, Anwarud Din
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in MMNSA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in MMNSA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
