New Bayesian Estimators for Randomized Response Technique

Akinola Oladiran Adepetun, Amos Adedayo Adewara

Abstract

This paper proposed new Bayesian estimators of the population proportion of a sensitive attribute when life data were collected through the administration of questionnaires on abortion on 300 matured women in some selected hospitals in the metropolis. Assuming both the Kumaraswamy (KUMA) and the generalised (GLS) beta distributions as alternative beta priors, efficiency of the proposed Bayesian estimators was established for a wide interval of the values of the population proportion (. We observed that for small, medium as well as large sample sizes, the developed Bayesian estimators were better in capturing responses from respondents than the conventional simple beta estimator proposed by Hussain and Shabbir (2009a) as  approaches one.

 

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References

Adepetun, A.O., Adewara, A.A. (2014): Bayesian Analysis of Kim and Warde Randomized Response Technique Using Alternative Priors. American Journal of Computational and Applied Mathematics, 4(4): 130-140.

Adebola, F.B. and Adepetun, A.O. (2011): A new Tripartite Randomized Response Technique. Journal of the Nigerian Association of Mathematical Physics, 19: 119-122.

Adebola,F.B. and Adepetun, A.O. (2012): On a Qualitative Comparison of the Proposed Randomized Response Technique with Hussain and Shabbir (2007). International Journal of Mathematical Theory and Modeling, 2: 61-67.

Adepetun, A.O. and Adebola, F.B. (2014): On the Relative Efficiency of the Proposed Reparametized Randomized Response Model. International Journal of Mathematical Theory and Modeling, 4: 58-67.

Bar-Lev, S.K. Bobovich, E. and Boukai, B. (2003): A common conjugate prior structure for several randomized response models. Test, 12(1), 101-113.

Barabesi, L., Marcheselli, M. (2006): A practical implementation and Bayesian estimation in Franklin’s randomized response procedure. Communication in Statistics- Simulation and Computation, 35, 365-573.

Christofides, T.C. (2003): A generalized randomized response technique. Metrika, 57, 195-200.

Greenberg, B., Abul-Ela, A., Simmons, W., Horvitz, D. (1969): The unrelated question randomized response: theoretical framework. Journal of the American Statistical Association, 64, 529-539.

Hussain, Z. and Shabbir, J. (2007): Randomized use of Warner’s randomized response model. InterStat: April # 7. http://interstat.statjournals.net/INDEX/Apr07.html

Hussain, Z., Shabbir, J. (2009a): Bayesian estimation of population proportion of a sensitive characteristic using simple Beta prior. Pakistan Journal of Statistics, 25(1), 27-35.

Hussain, Z., Shabbir, J. (2009b): Bayesian Estimation of population proportion in Kim and Warde (2005) Mixed Randomized Response using Mixed Prior Distribution. Journal of probability and Statistical Sciences, 7(1), 71-80.

Hussain, Z., Shabbir, J. (2012): Bayesian Estimation of population proportion in Kim and Warde Mixed Randomized Response Technique. Electronic Journal of Applied Statistical Analysis, 5(2), 213 – 225.

Kim, J. M., Tebbs, J. M., An, S. W. (2006): Extension of Mangat’s randomized response model. Journal of Statistical Planning and Inference, 36(4), 1554-1567.

Kim, J.M. and Warde, D.W. (2004): A stratified Warner’s Randomized Response Model. J. Statist. Plann. Inference, 120(1-2), 155-165.

Mangat, N.S. (1994): An improved randomized response strategy. J. Roy. Statist. Soc. Ser. B, 56(1), 93-95.

Mangat, N.S. and Singh, R. (1990): An alternative randomized response procedure. Biometrika. 77, 439-442.

Migon, H., Tachibana, V. (1997): Bayesian approximations in randomized response models. Computational Statistics and Data Analysis, 24, 401-409.

O’Hagan, A. (1987): Bayes linear estimators for randomized response models. Journal of the American Statistical Association, 82, 580-585.

Oh, M. (1994): Bayesian analysis of randomized response models: a Gibbs sampling approach. Journal of the Korean Statistical Society, 23, 463-482.

Pitz. G. (1980): Bayesian analysis of randomized response models. J. Psychological Bull, 87, 209-212.

Singh et al (1998): Estimation of stigmatized characteristics of a hidden gang in finite population. Austral. & New Zealand J. Statist, 40(3), 291-297.

Spurrier, J., Padgett, W. (1980): The application of Bayesian techniques in randomized response. Sociological Methodology, 11, 533-544.

Unnikrishnan, N., Kunte, S. (1999): Bayesian analysis for randomized response models. Sankhya, B, 61, 422-432.

Warner, S.L. (1965): Randomized Response: a survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc., 60, 63-69.

Winkler, R., Franklin, L. (1979): Warner’s randomized response model: A Bayesian approach. Journal of the American Statistical Association, 74, 207-214.

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