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An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable

Year 2016, Volume: 45 Issue: 2, 593 - 608, 01.04.2016

Abstract

In this paper, we have suggested a new randomized response model
and its properties have been studied. The proposed model is found
to be more efficient than the randomized response models studied by
Bar – Lev et al. (2004) and Eichhorn and Hayre (1983). The relative
efficiency of the proposed model has been studied with respect to the
Bar – Lev et al.’s (2004) and Eichhorn and Hayre’s (1983) models.
Numerical illustrations are also given to support the present study. 

References

  • Ahsanullah M. and Eichhorn B.H. (1988). On estimation of response from scrambled quantitative data. Pakistan Journal of Statistics, 4(2), 83-91.
  • Bar –Lev S.K., Bobovitch E. and Boukai B. (2004). A note on Randomized response models for quantitative data. Metrika, 60, 225-250.
  • Chaudhuri A. and Mukerjee R. (1988). Randomized Response: Theory and Techniques. Marcel- Dekker, New York, USA.
  • Chaudhuri A. and Christofides T. (2013). Indirect Questioning in Sample Surveys. DOI 10.1007/978-3-642-36276-7-3, Springer – Verlag Berlin Heidelberg.
  • Eichhorn B.H. and Hayre, L.S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistics Planning and Inference,7,307-316.
  • Fox J.A. and Tracy P.E. (1986). Randomized Response: A method of Sensitive Surveys. Newbury Park, CA: SEGE Publications.
  • Gjestvang C.R. and Singh S. (2006). A new randomized response model. Journal of the Royal Statistical Society, 68, 523-530.
  • Gjestvang C.R. and Singh S. (2009). An improved randomized response model: Estimation of mean, Journal of Applied Statistics, 36(12), 1361-1367.
  • Gleser L.J. and Healy J.D. (1976). Estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association, 71,977-981.
  • Govindaragulu Z. and Sahai H. (1972). Estimation of the parameters of a normal distribution with known coefficient of variation. Republic Statistics and Applications and Research, JUSU, 19,86-98.
  • Gupta S. and Thornton B. (2002). Circumventing social desirability response bias in personal interview surveys. American Journal of Mathematics Managment and Sciences, 22, 369-383.
  • Hussain Z., Hamraz M. and shabbier J. (2013) . On alternative estimation technique for randomized response model. Pakistan Journal of Statistics, 29(3), 283-306.
  • Hussain Z., Mashail, A.M., Bander A., Singh H.P. and Tarray T.A.(2015). Improved randomized response approaches for additive scrambling models . Mathematical Population Studiies. (In Press).
  • Khan RA (1968). A note on estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association, 63,1039-1041.
  • Kerkvliet J.(1994). Estimating a logit model with randomized data: the case of cocaine use. Austrialian Journal of Statistics,36,9-20.
  • Mangat N.S. and Singh R. (1990). An alternative randomized procedure. Biometrika, 77, 439-442.
  • Odumade O. and Singh S. (2009). Improved Bar – lev, Bobovitch and Boukai randomized response models. Communication in Statistics Theory and Methods, 38(3), 473-502.
  • Searls D. T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 12225-12226.
  • Sen A.R. (1978). Estimation of the mean when the coefficient of variation is known. Communication in Statistics Theory and Methods, 7(7), 657-672.
  • Sen A.R. (1979). Relative efficiency of the estimators of the mean of a normal distribution when coefficient of variation is known. Biometrical. Journal,21(2), 131-137.
  • Singh S. and Cheng S.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. Journal of Statististics Planning and Inference,139, 3377- 3380.
  • Singh H.P. and Katiyar N.P. (1988). A generalized class of estimators for common parameters of two normal distributions with known coefficient of variation. Journal of the Indian Society of the Agricultural Statistics, 40, (2), 127-149.
  • Singh H.P. and Mathur N. (2005). Estimation of population mean when coefficient of variation is known using scrambled response technique. Journal of Statististics Planning and Inference,131 (1), 135-144.
  • Singh H.P. and Tarray T.A. (2013). A modified survey technique for estimating the proportion and sensitivity in a dichotomous finite population. International Journal of the Advanved Science and and Technology Research, 3(6), 459 – 472.
  • Singh H.P. and Tarray T.A. (2014). An alternative to stratified Kim and Warde’s randomized response model using optimal (Neyman) allocation. Model Assisted Statistical Applications, 9, 37-62.
  • Singh H.P. and Tarray T.A. (2015). An efficient use of moment’s ratios of scrambling variables in randomized response sampling. Communication in Statistics Theory and Methods, (In Press).
  • Tarray T.A. and Singh H.P. and (2015). An improved new additive model. Gazi University Journal of Sciences, (In Press).
  • Tarray T.A., Singh H.P. and Zaizai Y. (2015). A stratified optional randomized response model. Sociological Methods and Research, 1-15.
  • Tripathi T.P., Maiti P. and Sharma S.D. (1983). Use of prior information on some parameters in estimating population mean . Sankhya, 45, A, 3, 372-376.
  • Upadhyaya L.N. and Singh H.P. (1984) . On the estimation of the population mean with known coefficient variation. Biometrical Journal, 26, (8), 915-922.
  • Warner S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60, 63-69.
Year 2016, Volume: 45 Issue: 2, 593 - 608, 01.04.2016

Abstract

References

  • Ahsanullah M. and Eichhorn B.H. (1988). On estimation of response from scrambled quantitative data. Pakistan Journal of Statistics, 4(2), 83-91.
  • Bar –Lev S.K., Bobovitch E. and Boukai B. (2004). A note on Randomized response models for quantitative data. Metrika, 60, 225-250.
  • Chaudhuri A. and Mukerjee R. (1988). Randomized Response: Theory and Techniques. Marcel- Dekker, New York, USA.
  • Chaudhuri A. and Christofides T. (2013). Indirect Questioning in Sample Surveys. DOI 10.1007/978-3-642-36276-7-3, Springer – Verlag Berlin Heidelberg.
  • Eichhorn B.H. and Hayre, L.S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistics Planning and Inference,7,307-316.
  • Fox J.A. and Tracy P.E. (1986). Randomized Response: A method of Sensitive Surveys. Newbury Park, CA: SEGE Publications.
  • Gjestvang C.R. and Singh S. (2006). A new randomized response model. Journal of the Royal Statistical Society, 68, 523-530.
  • Gjestvang C.R. and Singh S. (2009). An improved randomized response model: Estimation of mean, Journal of Applied Statistics, 36(12), 1361-1367.
  • Gleser L.J. and Healy J.D. (1976). Estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association, 71,977-981.
  • Govindaragulu Z. and Sahai H. (1972). Estimation of the parameters of a normal distribution with known coefficient of variation. Republic Statistics and Applications and Research, JUSU, 19,86-98.
  • Gupta S. and Thornton B. (2002). Circumventing social desirability response bias in personal interview surveys. American Journal of Mathematics Managment and Sciences, 22, 369-383.
  • Hussain Z., Hamraz M. and shabbier J. (2013) . On alternative estimation technique for randomized response model. Pakistan Journal of Statistics, 29(3), 283-306.
  • Hussain Z., Mashail, A.M., Bander A., Singh H.P. and Tarray T.A.(2015). Improved randomized response approaches for additive scrambling models . Mathematical Population Studiies. (In Press).
  • Khan RA (1968). A note on estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association, 63,1039-1041.
  • Kerkvliet J.(1994). Estimating a logit model with randomized data: the case of cocaine use. Austrialian Journal of Statistics,36,9-20.
  • Mangat N.S. and Singh R. (1990). An alternative randomized procedure. Biometrika, 77, 439-442.
  • Odumade O. and Singh S. (2009). Improved Bar – lev, Bobovitch and Boukai randomized response models. Communication in Statistics Theory and Methods, 38(3), 473-502.
  • Searls D. T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 12225-12226.
  • Sen A.R. (1978). Estimation of the mean when the coefficient of variation is known. Communication in Statistics Theory and Methods, 7(7), 657-672.
  • Sen A.R. (1979). Relative efficiency of the estimators of the mean of a normal distribution when coefficient of variation is known. Biometrical. Journal,21(2), 131-137.
  • Singh S. and Cheng S.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. Journal of Statististics Planning and Inference,139, 3377- 3380.
  • Singh H.P. and Katiyar N.P. (1988). A generalized class of estimators for common parameters of two normal distributions with known coefficient of variation. Journal of the Indian Society of the Agricultural Statistics, 40, (2), 127-149.
  • Singh H.P. and Mathur N. (2005). Estimation of population mean when coefficient of variation is known using scrambled response technique. Journal of Statististics Planning and Inference,131 (1), 135-144.
  • Singh H.P. and Tarray T.A. (2013). A modified survey technique for estimating the proportion and sensitivity in a dichotomous finite population. International Journal of the Advanved Science and and Technology Research, 3(6), 459 – 472.
  • Singh H.P. and Tarray T.A. (2014). An alternative to stratified Kim and Warde’s randomized response model using optimal (Neyman) allocation. Model Assisted Statistical Applications, 9, 37-62.
  • Singh H.P. and Tarray T.A. (2015). An efficient use of moment’s ratios of scrambling variables in randomized response sampling. Communication in Statistics Theory and Methods, (In Press).
  • Tarray T.A. and Singh H.P. and (2015). An improved new additive model. Gazi University Journal of Sciences, (In Press).
  • Tarray T.A., Singh H.P. and Zaizai Y. (2015). A stratified optional randomized response model. Sociological Methods and Research, 1-15.
  • Tripathi T.P., Maiti P. and Sharma S.D. (1983). Use of prior information on some parameters in estimating population mean . Sankhya, 45, A, 3, 372-376.
  • Upadhyaya L.N. and Singh H.P. (1984) . On the estimation of the population mean with known coefficient variation. Biometrical Journal, 26, (8), 915-922.
  • Warner S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60, 63-69.
There are 31 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Housila P. Singh This is me

Tanveer A Tarray

Publication Date April 1, 2016
Published in Issue Year 2016 Volume: 45 Issue: 2

Cite

APA P. Singh, H., & Tarray, T. A. (2016). An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable. Hacettepe Journal of Mathematics and Statistics, 45(2), 593-608.
AMA P. Singh H, Tarray TA. An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable. Hacettepe Journal of Mathematics and Statistics. April 2016;45(2):593-608.
Chicago P. Singh, Housila, and Tanveer A Tarray. “An Improved Bar - Lev, Bobovitch and Boukai Randomized Response Model Using Moments Ratios of Scrambling Variable”. Hacettepe Journal of Mathematics and Statistics 45, no. 2 (April 2016): 593-608.
EndNote P. Singh H, Tarray TA (April 1, 2016) An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable. Hacettepe Journal of Mathematics and Statistics 45 2 593–608.
IEEE H. P. Singh and T. A. Tarray, “An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 593–608, 2016.
ISNAD P. Singh, Housila - Tarray, Tanveer A. “An Improved Bar - Lev, Bobovitch and Boukai Randomized Response Model Using Moments Ratios of Scrambling Variable”. Hacettepe Journal of Mathematics and Statistics 45/2 (April 2016), 593-608.
JAMA P. Singh H, Tarray TA. An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable. Hacettepe Journal of Mathematics and Statistics. 2016;45:593–608.
MLA P. Singh, Housila and Tanveer A Tarray. “An Improved Bar - Lev, Bobovitch and Boukai Randomized Response Model Using Moments Ratios of Scrambling Variable”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, 2016, pp. 593-08.
Vancouver P. Singh H, Tarray TA. An Improved Bar - Lev, Bobovitch and Boukai randomized response model using moments ratios of scrambling variable. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):593-608.