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
Housila P. Singh
Tanveer A Tarray
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
Housila P. Singh
Tanveer A Tarray
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.