A simple way of improving the Bar–Lev, Bobovitch and Boukai Randomized response model
Keywords:Estimation of proportion, randomized response sampling, respondents protection, sensitive quantitative variable.
Eichhorn & Hayre (1983) considered a randomized response procedure suitable for estimating the mean response, when the sensitive variable under investigation is quantitative in nature. They have obtained an estimate for the mean of the quantitative response variable under investigation and studied its properties. Bar–Lev et al. (2004) have suggested an alternative procedure, which use a design parameter (controlled by the experimenter) that generalizes Eichhorn & Hayre’s (1983) results. They have also proved that the estimator proposed by them has uniformly smaller variance as compared to that of Eichhorn & Hayre (1983) in certain condition. In this paper we have suggested a simple procedure of improving the Eichhorn & Hayre (1983) and Bar–Lev et al. (2004) models along with its properties. It has been shown that the proposed procedure is uniformly better than Bar–Lev et al. (2004) procedure. The proposed procedure is also uniformly better than Eichhorn and Hayre’s (1983) procedure under the same condition in which the Bar–Lev et al.’s (2004) procedure is more efficient than Eichhorn & Hayre’s (1983) procedure. Numerical illustration is given in support of the present study.
Chaudhuri, A. & Mukerjee, R. (1988). Randomized
response: Theory and techniques. Marcel- Dekker, New
Bar –Lev,SKE., Bobovitch, E. & Boukai, B. (2004). A
note on randomized responsemodels for quantitative data.
Metrika, 60:225 -250.
Eichhorn, B.H. & Hayre, L.S. (1983). Scrambled
randomized response methods for obtaining sensitive
quantitative dada. Journal of Statistics and planning
Inference, 7:307 -316.
Fox, J.A. & Tracy, P.E. (1986). Randomized Response:
A method of Sensitive Surveys. Newbury Park, CA:
Gjestvang, C.R. & Singh, S. (2006). A new randomized
response model. Journal of Royal Statistical Society, 68:
Gjestvang, C.R. & Singh, S. (2009). An improved
randomized response model: Estimation of mean,
Journal of Applied Statistics, 36(12): 1361 -1367.
Hussain, Z. (2012). Improvement of Gupta and
Thornton scrambling model through double use of
randomization device. International Journal of Academic
ResearchBusiness and Society and Science, 2(6),91 -97.
Odumade, O. & Singh, S. (2008). Generalized forced
quantitative randomized response model: A unified
approach. Journal of Indian Society of Agricultural and
Statistics, 62(3): 244 -252.
Odumade, O. & Singh, S. (2009). Improved Bar-Lev,
Bobovitch and Boukai randomized response models.
Communication in Statistics andTheory and .
Methods, 38(3):473 -502.
Singh, H.P. & Mathur, N. (2004). Estimation of
population mean with known coefficient of variation
under optional response model using scrambled response
technique.Statistics and Transactions, 6 (7):1079 -1093.
Singh, H.P. & Mathur, N. (2005). Estimation of
population mean when coefficient ofvariation is known
using scrambled response technique. Journal of
Statistics and Planning Inference, 131:135 -144.
Singh, H.P. & Tarray, T.A.(2013). A modified survey
technique for estimating the proportion and sensitivity in
a dichotomous finite population.International
Journal of Advanced Sciences and Technology Research,
(6):459 – 472.
Singh, H.P. & 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,
Singh, S. (2003). Advanced sampling theory with
applications. Kluwer Academic Publishers, Dordrecht,
Tarray, T.A. & Singh, H.P. (2015). Some improved
additive randomized response models utilizing higher
order moments ratios of scrambling variable. Model
Assisted Statistics and Applications, 10:361 -383.
Tarray, T.A. & Singh, H.P. (2016). An adroit randomized
response new additive scrambling model. Gazi University
Journal of Sciences, 29(1):159 -165.
Tarray, T.A. & Singh, H.P. (2017). A Survey Technique
for Estimating the Proportion and Sensitivity in a
Stratified Dichotomous Finite Population.
Statistics and Applications, 15(1,2):173 -191.
Warner, S.L. (1965). Randomized response: A survey
technique for eliminating evasive answer bias. Journal of
American Statistical Association, 60:63 -69.