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Journal of Statistical Theory and Practice

, Volume 9, Issue 3, pp 633–645 | Cite as

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

  • Geeta Kalucha
  • Sat Gupta
  • B. K. Dass
Article

Abstract

Auxiliary information is commonly used in sample surveys in order to achieve higher precision in the estimates. In this article we are concerned with the utilization of auxiliary information in the estimation stage in simple random sampling without replacement (SRSWOR), making use of an optional randomized response model proposed by Gupta et al. (2010). The underlying assumption is that the primary variable is sensitive in nature but a nonsensitive auxiliary variable exists that is positively correlated with the primary variable. We propose a ratio estimator of finite population mean and call it the additive ratio estimator. Expressions for the bias and mean square error of the proposed estimator are obtained to first order of approximation. Efficiency comparisons with the ordinary optional randomized response technique (RRT) mean estimator of Gupta et al. (2010) are carried out both theoretically and numerically. A simulation study is presented to evaluate the performance of the proposed estimator.

Keywords

Auxiliary information Mean square error Randomized response technique Ratio estimator Optional ORR models 

AMS Subject Classification

62D05 

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References

  1. Eichhron, B.H., and L.S. Hayre. 1983. Scrambled randomized response methods for obtaining sensitive quantitative data. J. Stat. Plan. Inference 7:307–316.CrossRefGoogle Scholar
  2. Eriksson, S.A. 1973. A new model for randomized response. Int. Stat. Rev. 41(1):101–113.CrossRefGoogle Scholar
  3. Greenberg, B.G., A.-L. A. Abul-Ela, W.R. Simmons, and H.G. Hoevitz. 1969. The unrelated question randomized response model: Theoretical framework. J. Am. Stat. Assoc. 64:520–539.MathSciNetCrossRefGoogle Scholar
  4. Gupta, S., J. Shabbir, and S. Sehra. 2010. Mean and sensitivity estimation in optional randomized response models. J. Stat. Plan. Inference 140(10):2870–2874.MathSciNetCrossRefGoogle Scholar
  5. Gupta, S., S. Mehta, J. Shabbir, and B.K. Dass. 2013. Generalized scrambling in quantitative optional randomized response models. Commun. Stat. Theory Methods 42(20):1–9.MathSciNetzbMATHGoogle Scholar
  6. Gupta, S.N., B.C. Gupta, and S. Singh. 2002. Estimation of sensitivity level of personnel interview survey questions. J. Stat. Plan. Inference 100:239–247.CrossRefGoogle Scholar
  7. Huang, K.C. 2010. Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling. Metrika 71:341–352.MathSciNetCrossRefGoogle Scholar
  8. Kadilar, C., and H. Cingi. 2006. Improvement in estimating the population mean in simple random sampling. Appl. Math. Lett. 19(1):75–79.MathSciNetCrossRefGoogle Scholar
  9. Kim, J.M., and W.D. Warde. 2005. A stratified Warner’s randomized response model, J. Stat. Plan. Inference 120(1–2): 155–165.MathSciNetzbMATHGoogle Scholar
  10. Kim, J.M., Warde, W. D. 2004. A mixed randomized response model. J. Stat. Plan. Inference 133(1):211–221.MathSciNetCrossRefGoogle Scholar
  11. Koyuncy, N., and C. Kadilar. 2009. Efficient estimators for the population mean. Hacettepe J. Math. Stat. 38(2):217–225.MathSciNetzbMATHGoogle Scholar
  12. Saha, A. 2008. A randomized response technique for quantitative data under unequal probability sampling. J. Stat. Theory Pract. 2(4):589–596.MathSciNetCrossRefGoogle Scholar
  13. Sousa, R., J. Shabbir, R. Corte-Real, and S. Gupta. 2010. Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information. J. Stat. Theory Pract. 4(3):495–507.MathSciNetCrossRefGoogle Scholar
  14. van der Heijden, P.G.M., G. van Gils, J. Bouts, and J.J. Hox. 2000. A comparison of randomized response, computer-assisted self-interview and face-to-face direct questioning: Eliciting sensitive information in the context of welfare and unemployment benefit. Sociol. Methods Res. 28:505–537.CrossRefGoogle Scholar
  15. Sukhatme, P.V., and B.V. Sukhatme. 1970. Sampling Theory of Surveys with Applications. Ames, IA: Iowa State University Press.zbMATHGoogle Scholar
  16. Warner, S. L. 1965. Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhi, NoidaIndia
  2. 2.Department of Mathematics and StatisticsUniversity of North Carolina at GreensboroGreensboroUSA

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