Abstract
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).
An efficient application of scrambled response approach to estimate the population mean of the sensitive variables
Abstract
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.
Keywords
Randomized response technique simple random sampling scrambling response sensitive and non-sensitive variables exponential-type estimators
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).
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | September 30, 2022 |
| Submission Date | May 25, 2022 |
| Published in Issue | Year 2022 Volume: 2 Issue: 3 |
Cited By
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