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Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model. (English) Zbl 1508.62022

Summary: J. S. Sihm et al. [Involve 9, No. 2, 195–209 (2016; Zbl 1334.62025)] proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. [loc. cit.]. The results obtained are illustrated with the help of real survey data using non informative prior.

MSC:

62D05 Sampling theory, sample surveys
62F15 Bayesian inference

Citations:

Zbl 1334.62025
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References:

[1] Barabesi, L., and M. Maecheselli. 2010. Bayesian estimation of proportion and sensitivity level in randomized response procedures. Metrika 72:75-88. · Zbl 1189.62041 · doi:10.1007/s00184-009-0242-7
[2] Chhabra, A., B. K. Dass, and S. Gupta. 2016a. Estimating Prevalence of sexual abuse by an acquaintance with an optional unrelated question RRT model. North Carolina Journal of Mathematics and Statistics 2:1-9.
[3] Chhabra, A., B. K. Dass, and S. Mehta. 2016b. Multi-stage optional unrelated question RRT model. Journal of Statistical Theory and Applications 15 (1):80-95. · doi:10.2991/jsta.2016.15.1.7
[4] Greenberg, B. G., A. L. A. Abul-Ela, W. R.Simmons and D. G. Horvitz. 1969. The unrelated question randomized response model: Theoretical framework. Journal of the American Statistical Association 64:520-29.
[5] Gupta, S. N., B. C. Gupta, and S. Singh. 2002. Estimation of sensitivity level of personal interview survey questions. Journal of Statistical Planning and Inference 100:239-247. · Zbl 0985.62010 · doi:10.1016/S0378-3758(01)00137-9
[6] Gupta, S. N., A. Tuck, T. Spears Gill, and M. Crowe. 2013. Optional unrelated question randomized response models. Involve: A Journal of Mathematics 6 (4):483-492. · Zbl 1293.62021 · doi:10.2140/involve.2013.6.483
[7] Kim, J. M., J. M. Tebbs, and S. W. An. 2006. Extensions of Mangat’s randomized response model. Journal of Statistical Planning and Inference 36 (4):1554-1567. · Zbl 1088.62014 · doi:10.1016/j.jspi.2004.10.005
[8] Mangat, N. S., and R. Singh. 1990. An alternative randomized response procedure. Biometrika 77:439-442. · Zbl 0713.62011 · doi:10.1093/biomet/77.2.439
[9] Mehta, S., B. K. Dass, J. Shabbir, and S. N. Gupta. 2012. A three stage optional randomized response model. Journal of Statistical Theory and Practice 6 (3):417-427. · Zbl 1425.62018
[10] Nayak, T. N., and S. A. Adeshiyan. 2009. A unified framework for analysis and comparison of randomized response surveys of binary characteristics. Journal of Statistical Planning and Inference 139:2757-2766. · Zbl 1162.62004 · doi:10.1016/j.jspi.2008.12.013
[11] O’Hagan, A. 1987. Bayes linear estimators for randomized response models. Journal of the American Statistical Association 82:580-585. · Zbl 0657.62011
[12] Sihm, J. S., A. Chhabra, and S. N. Gupta. 2016. An optional unrelated question RRT model. Involve: A Journal of Mathematics 9 (2):195-209. · Zbl 1334.62025 · doi:10.2140/involve.2016.9.195
[13] Unnikrishnan, N., and S. Kunte. 1999. Bayesian analysis for randomized response models. Sankhya Series B 61:422-432. · Zbl 0981.62007
[14] Warner, S. L. 1965. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association 60:63-69. · Zbl 1298.62024
[15] Winkler, R., and L. Franklin. 1979. Warner’s randomized response model: A Bayesian approach. Journal of the American Statistical Association 74:207-214.
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