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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.

Anahtar Kelimeler

Randomized response models Sensitive question Auxiliary variable Efficiency Mean square error

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

Öz

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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm İstatistik
Yazarlar

Nilgun Ozgul

Hulya Cingi

Yayımlanma Tarihi 1 Nisan 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 2

Kaynak Göster

APA Ozgul, N., & Cingi, H. (2017). A new improved estimator of population mean in partial additive randomized response models. Hacettepe Journal of Mathematics and Statistics, 46(2), 325-338.
AMA Ozgul N, Cingi H. A new improved estimator of population mean in partial additive randomized response models. Hacettepe Journal of Mathematics and Statistics. Nisan 2017;46(2):325-338.
Chicago Ozgul, Nilgun, ve Hulya Cingi. “A New Improved Estimator of Population Mean in Partial Additive Randomized Response Models”. Hacettepe Journal of Mathematics and Statistics 46, sy. 2 (Nisan 2017): 325-38.
EndNote Ozgul N, Cingi H (01 Nisan 2017) A new improved estimator of population mean in partial additive randomized response models. Hacettepe Journal of Mathematics and Statistics 46 2 325–338.
IEEE N. Ozgul ve H. Cingi, “A new improved estimator of population mean in partial additive randomized response models”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 2, ss. 325–338, 2017.
ISNAD Ozgul, Nilgun - Cingi, Hulya. “A New Improved Estimator of Population Mean in Partial Additive Randomized Response Models”. Hacettepe Journal of Mathematics and Statistics 46/2 (Nisan 2017), 325-338.
JAMA Ozgul N, Cingi H. A new improved estimator of population mean in partial additive randomized response models. Hacettepe Journal of Mathematics and Statistics. 2017;46:325–338.
MLA Ozgul, Nilgun ve Hulya Cingi. “A New Improved Estimator of Population Mean in Partial Additive Randomized Response Models”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 2, 2017, ss. 325-38.
Vancouver Ozgul N, Cingi H. A new improved estimator of population mean in partial additive randomized response models. Hacettepe Journal of Mathematics and Statistics. 2017;46(2):325-38.

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