A new improved estimator of population mean in partial additive randomized response models
Yıl 2017,
Cilt: 46 Sayı: 2, 325 - 338, 01.04.2017
Nilgun Ozgul
,
Hulya Cingi
Öz
In this study, we have developed a new improved estimator for the population mean estimation of the sensitive study variable in Partial Additive Randomized Response Models (RRMs) using two non-sensitive auxiliary variables. The mean squared error of the proposed estimator is derived and compared with other existing estimators based on the auxiliary variable. The proposed estimator is compared with [19], [5] and [13] estimators in performing a simulation study and is found to be more efficient than other existing estimators using non-sensitive auxiliary variable. The results of the simulation study are discussed in the final section.
Kaynakça
- Bar-Lev S.K., Bobovitch E., Boukai B. A note on randomized response models for quanti-
tative data. Metrika 60, 255-260, 2004.
- Cingi, H. Ornekleme Kuram. Ankara: 3.Baski, Bizim Buro Basimevi, 2009.
- Cingi, H. and Kadilar, C.Advances in Sampling Theory-Ratio Method of Estimation .Ben-
tham Science Publishers,121, 2009.
- Diana G., Perri P.F.New Scrambled Response Models For Estimating The Mean of A Sen-
sitive Quantitative Character.Journal Of Applied Statistics ,37 (11), 1875-1890, 2010.
- Diana G., Perri P.F. A class of Estimators for Quantitative Sensitive Data.Statistical Pa-
pers,52, 633-650, 2011.
- Eichhorn, B. H. and Hayre, L. S.Scrambled Randomized Response Methods for Obtaining
Sensitive Quantitative Data. Journal of Statistical Planning and Inference , 7 (1) ,307-316,
1983.
- Gjesvang, C.R., Singh,S. An improved Randomized Response Model:Estimation of Mean.
Journal of Applied Statistics, 36 (12),1361-1367, 2009.
- Greenberg B.G., Kuebler R.R., Abernathy J.R., Horvitz D.G.Application of the randomized
response technique in obtaining quantitative data. Journal of American Statistical Associa-
tion , 66, 243-250, 1971.
- Gupta S., Gupta B., Singh S. Estimation of sensitivity level of personal interview survey
questions. J. Stat Plan Inference ,100, 239-247, 2002.
- Gupta, S.N. and Shabbir, J. Sensitivity estimation for personal interview survey Questions.
Statistica,64, 643-653, 2004.
- Gupta, S. N. and Shabbir,J. On the Estimation of Population Mean and Sensitivity in
Two-stage Optional Randomized Response Model. Journal of Indian Society of Agricultural
Statistics, 61, 164-168, 2007.
- Gupta S., Shabbir J., Sousa R. and Sehra S. Mean and sensitivity estimation in optional
randomized response model.Communications in Statistics , 140, 2870-2874, 2010.
- Gupta, S., Shabbir, J., Sousa, R., Real, P. C. Estimation of the mean of a sensitive vari-
able in the presence of auxiliary information. Communications in Statistics, Theory and
Methods, 41, 1-12, 2012.
- Hussain Z., Shabbir, J.Improved Estimation Procedures for the Mean of Sensitive Variable
using Randomized Response Model . Pak.J.Statist.25(2), 205-220, 2009.
- Ozgul, N. Proportion and Mean Estimators in Randomized Response Models, Ph.D. Thesis.
Hacettepe University, Ankara, 2013.
- Ryu J.-B, Kim J.-M, Heo T-Y, Park C. G. On stratified Randomized Response Sampling.
Model Assisted Statistics and Application 1(1): 31-36, 2005.
- Saha, A.A simple randomized response technique in complex surveys. Metron LXV,59-66,
2007.
- Sehra, Supriti, M.A. Two-Stage Optional Randomized Response Models, Master of Art
Dissertation. The University of North Carolina, Greensboro, U.S.A, 2008.
- Sousa, R., Shabbir, J. Real, P. C. and Gupta, S.Ratio estimation of the mean of a sensitive
variable in the presence of auxiliary information . Journal of Statistical Theory and Practice,
4(3), 495-507, 2010.
- Thornton, B. and Gupta, S. N. Comparative Validation of a Partial (versus Full) Random-
ized Response Technique: Attempting to Control for Social Desirability Response Bias to
Sensitive Questions. Individual Dierences Research, 2, 214-224, 2004.
- Warner, S.L. Randomized response: A survey technique for eliminating evasive answer bias.
Journal of the American Statistical Association, 60, 63-69, 1965.
- Warner, S.L. The Linear Randomized Response Model, Journal of the American Statistical
Association 66(336), 884-888, 1971.
Yıl 2017,
Cilt: 46 Sayı: 2, 325 - 338, 01.04.2017
Nilgun Ozgul
,
Hulya Cingi
Kaynakça
- Bar-Lev S.K., Bobovitch E., Boukai B. A note on randomized response models for quanti-
tative data. Metrika 60, 255-260, 2004.
- Cingi, H. Ornekleme Kuram. Ankara: 3.Baski, Bizim Buro Basimevi, 2009.
- Cingi, H. and Kadilar, C.Advances in Sampling Theory-Ratio Method of Estimation .Ben-
tham Science Publishers,121, 2009.
- Diana G., Perri P.F.New Scrambled Response Models For Estimating The Mean of A Sen-
sitive Quantitative Character.Journal Of Applied Statistics ,37 (11), 1875-1890, 2010.
- Diana G., Perri P.F. A class of Estimators for Quantitative Sensitive Data.Statistical Pa-
pers,52, 633-650, 2011.
- Eichhorn, B. H. and Hayre, L. S.Scrambled Randomized Response Methods for Obtaining
Sensitive Quantitative Data. Journal of Statistical Planning and Inference , 7 (1) ,307-316,
1983.
- Gjesvang, C.R., Singh,S. An improved Randomized Response Model:Estimation of Mean.
Journal of Applied Statistics, 36 (12),1361-1367, 2009.
- Greenberg B.G., Kuebler R.R., Abernathy J.R., Horvitz D.G.Application of the randomized
response technique in obtaining quantitative data. Journal of American Statistical Associa-
tion , 66, 243-250, 1971.
- Gupta S., Gupta B., Singh S. Estimation of sensitivity level of personal interview survey
questions. J. Stat Plan Inference ,100, 239-247, 2002.
- Gupta, S.N. and Shabbir, J. Sensitivity estimation for personal interview survey Questions.
Statistica,64, 643-653, 2004.
- Gupta, S. N. and Shabbir,J. On the Estimation of Population Mean and Sensitivity in
Two-stage Optional Randomized Response Model. Journal of Indian Society of Agricultural
Statistics, 61, 164-168, 2007.
- Gupta S., Shabbir J., Sousa R. and Sehra S. Mean and sensitivity estimation in optional
randomized response model.Communications in Statistics , 140, 2870-2874, 2010.
- Gupta, S., Shabbir, J., Sousa, R., Real, P. C. Estimation of the mean of a sensitive vari-
able in the presence of auxiliary information. Communications in Statistics, Theory and
Methods, 41, 1-12, 2012.
- Hussain Z., Shabbir, J.Improved Estimation Procedures for the Mean of Sensitive Variable
using Randomized Response Model . Pak.J.Statist.25(2), 205-220, 2009.
- Ozgul, N. Proportion and Mean Estimators in Randomized Response Models, Ph.D. Thesis.
Hacettepe University, Ankara, 2013.
- Ryu J.-B, Kim J.-M, Heo T-Y, Park C. G. On stratified Randomized Response Sampling.
Model Assisted Statistics and Application 1(1): 31-36, 2005.
- Saha, A.A simple randomized response technique in complex surveys. Metron LXV,59-66,
2007.
- Sehra, Supriti, M.A. Two-Stage Optional Randomized Response Models, Master of Art
Dissertation. The University of North Carolina, Greensboro, U.S.A, 2008.
- Sousa, R., Shabbir, J. Real, P. C. and Gupta, S.Ratio estimation of the mean of a sensitive
variable in the presence of auxiliary information . Journal of Statistical Theory and Practice,
4(3), 495-507, 2010.
- Thornton, B. and Gupta, S. N. Comparative Validation of a Partial (versus Full) Random-
ized Response Technique: Attempting to Control for Social Desirability Response Bias to
Sensitive Questions. Individual Dierences Research, 2, 214-224, 2004.
- Warner, S.L. Randomized response: A survey technique for eliminating evasive answer bias.
Journal of the American Statistical Association, 60, 63-69, 1965.
- Warner, S.L. The Linear Randomized Response Model, Journal of the American Statistical
Association 66(336), 884-888, 1971.