An alternative approach for construction of strata using quantified sensitivity level
Article Main
Abstract
The study is investigated on an alternative method for the construction of strata using sensitivity level when the samples are selected with simple random sampling with replacement (SRSWR) and the data are collected by scrambled optional randomization technique on the sensitive characters. Thus, the optional randomized response model , where k is a random variable having value 1 if the response is scrambled and 0 otherwise, was considered for finding out Approximate Optimum Strata Boundaries by minimizing the variance of the estimator . The cum. was proposed for finding out Approximate Optimum Strata Boundary in Neyman allocation for the optional scrambled response. This is applicable for wider classes of sampling design and estimators in stratification. The proposed rule on optional scrambled randomized response is efficient and can be used effectively for the construction of optimum strata boundary via Rectangular, Right triangular and Exponential distribution.
Article Details
Article Details
Approximate optimum strata boundary, Minimal equation, Neyman allocation, Optional randomization, Scrambled response, Sensitivity level
Arnab, R., Shangodoyin, D.K. & Kgosi P.M. (2017). Randomized response techniques with multiple responses. J. Ind. Soc. Agril. Statist., 71(3), 201–205.
Chandel, A., Mahajan, P. K. & Baharti (2016). Minimum variance stratification using scrambled randomised response. International Journal of Agricultural and Statistical Sciences, 12(1), 53-58.
Chaudhuri, A. & Mukherjee, R. (1987). Randomized response techniques: A review. Statistica Neerlandica, 41(1), 27-44. doi.org/10.1111/j.1467-9574.1987.tb01169.x
Chaudhuri, A. & Christofides, T C. 2013. Indirect Questioning in Sample Surveys. Heidelberg: Springer. doi.org/10.1007/978-3-642-36276-7
Dalenius T. (1950). The problem of optimum stratification. Skand. Aktuarietid Skrift, 33, 203-213. doi.org/10.1080/03 461238.1950.10432042
Fox, J. A. 2016. Randomized Response and Related Methods. Second Edition. California: SAGE Publications. doi.org/10.4135/9781506300122
Gjestvang, C.R. & Singh, S. (2006). A new randomized response model. Journal of The Royal Statistical Society B, 68, 523–530.
Greenberg, B.G., Kuelber, R. R., Abernathy, J. R. & Horvitz, D. G. (1971). Application of the randomized response technique in obtaining quantitative data. Journal of American Statistical Association, 66, 243-250.
Gupta, S., Gupta, B. & Singh, S. (2002). Estimation of sensitivity level of personal interview survey questions. J. Statist. Plann. Inference, 100, 239–247. doi.org/10.1016/S0378-3758(01)00137-9
Kumar A, Vishwakarma G. K. & Singh G. N. (2020). An improved randomized response model for simultaneous estimation of means of two quantitative sensitive variables. Comm. Statist. –simulation and computations, 1-21. doi.org/10.1080/03610918.2020.1788587
Mahajan, P.K., Gupta, J.P. & Singh, R. (1994). Determination of optimum strata boundaries for scrambled randomized response. Statistica Anno, 54(3), 376-381. doi.org/10.6092/issn.1973-2201/1023
Singh, R. & Prakash, D. (1975). Optimum stratification for equal allocation. Annals of Institute of Statistical Mathematics, 27, 273-280.
Singh, R. & Sukhatme, B.V. (1969). Optimum stratification. Annals of Institute of Statistical Mathematrica, 21, 515- 528.
Singh, H.P. & Gorey, S.M. (2019). A remark on Gupta, Gupta and Singh Optional Randomized Response Model, University of SS. JAMSI, 15 (1). doi.org/10.2478/jamsi-2019-0004
Singh, H. P. & Tarray, T A. 2014. An improved randomized response additive model. Srilankan J. Appl. Stat., 15(2), 131–138. doi.org/10.4038/sljastats.v15i2.7412
Tarray, T.A., Singh, H.P & Yan, Z. (2015). A dexterous optional randomized response model. Sociological Methods and Research, 46(3), 565-585. doi.org/10.1177/0049124115605332
Tarray, T.A. & Singh, H.P. (2017). An optional randomized response model for estimating a rare sensitive attribute using poisson distribution. Communications in Statistics-Theory and Methods, 46(6), 2638-2654. doi.org/10.1080/03610926.2015.1040506
Verma, M.R., Singh, S. & Pandey, R. 2012. Optimum stratification for sensitive quantitative variables using auxiliary information. J. Ind. Soc. Agril. Statist., 66(3), 401-412.
Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60, 63-69.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
This work is licensed under Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) © Author (s)