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Year 2007, Volume: 56 Issue: 1, 7 - 20, 01.02.2007

Yaprak Arzu Özdemir Alptekin Esin A.

https://doi.org/10.1501/Commua1_0000000194

Abstract

References

  • Barnett, V., Barreto, M.C.M., Best linear unbiased estimators for the simple linear regression model using ranked set sampling, Environmental and Ecological Statistics. 6 (1999), 119-133.
  • Bhattacharya, P.K., Convergence of sample paths of normalized sums of induced order sta- tistics, The Annnals of Statistics. 2 (1974), 1034-1039.
  • Chen, Z., Adaptive ranked-set sampling with multiple concomitant variables, Bernoulli. 8 (2002), 313-322.
  • Chen, Z., Bai, Z., Sinha, B.K., Ranked Set Sampling Theory and Applications, 2004, New York: Springer-Verlag.
  • Chen, Z., Wang, Y., E¢ cient regression analysis with ranked-set sampling, Biometrics. 60 (2004), 994-997.
  • Dell, D.R., Clutter, J.L., Ranked set sampling theory with order statistics background, Bio- metrics. 28 (1972), 545-555.
  • McIntyre, G.A., A method of unbiased selective sampling using ranked sets, Australian Jour- nal of Agricultural Research. 3 (1952), 385-390.
  • Muttlak, H.A., Parameters estimation in a simple linear regression using ranked set sampling, Biometrical Journal. 37 (1995), 799-810.
  • Muttlak, H.A., Estimation of parameters in a multiple regression model using ranked set sampling, Information and Optimization Sciences. 17 (1996), 521-533.
  • Özdemir, Y.A, Investigation of Parameter Estimation in Linear Regression Models Using Ranked Set Sampling, Gazi Üniversitesi Fen Bilimleri Enstitüsü, unpublished PhD thesis, (2005).
  • Samawi, H.M., Ababneh, F.M., On regression analysis using ranked set sample, Journal of Statistical Research. 35 (2001), 93-105.
  • Stokes, L.S., Ranked set sampling with concomitant variables, Commun. Statist. Theor. Meth. A6 (1977), 1207-1211.
  • Current address : Department of Statistics, Faculty of Science and Arts,University of Gazi, Be¸sevler, 06500, Ankara, Turkey

PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING

Year 2007, Volume: 56 Issue: 1, 7 - 20, 01.02.2007

Yaprak Arzu Özdemir Alptekin Esin A.

https://doi.org/10.1501/Commua1_0000000194

Abstract

In statistical surveys, if the measurements of sampling units according to the variable under consideration is expensive in all sense, and if itis possible to rank sampling units according to the same variable by means ofa method which is not expensive at all, in those cases, Ranked Set Sampling(RSS) is a more e¢ cient sampling method than the Simple Random Sampling(SRS) to estimate the population mean. In this study, the eğects of using RSSin multiple linear regression analysis are considered in terms of estimation ofmodel parameters. Firstly, according to RSS and SRS the estimates of multipleregression model parameters are obtained and then the eğects concerning thevariances of the estimators are investigated by Monte Carlo simulation studybased on Relative E¢ ciency (RE) measure. It is shown that the estimatorsobtained based on RSS are more e¢ cient than the estimators based on SRSwhen the sample size is small

Keywords

Simple Random Sampling Ranked Set Sampling Order Statistics Relative E¢ ciency Regression Analysis.

References

  • Barnett, V., Barreto, M.C.M., Best linear unbiased estimators for the simple linear regression model using ranked set sampling, Environmental and Ecological Statistics. 6 (1999), 119-133.
  • Bhattacharya, P.K., Convergence of sample paths of normalized sums of induced order sta- tistics, The Annnals of Statistics. 2 (1974), 1034-1039.
  • Chen, Z., Adaptive ranked-set sampling with multiple concomitant variables, Bernoulli. 8 (2002), 313-322.
  • Chen, Z., Bai, Z., Sinha, B.K., Ranked Set Sampling Theory and Applications, 2004, New York: Springer-Verlag.
  • Chen, Z., Wang, Y., E¢ cient regression analysis with ranked-set sampling, Biometrics. 60 (2004), 994-997.
  • Dell, D.R., Clutter, J.L., Ranked set sampling theory with order statistics background, Bio- metrics. 28 (1972), 545-555.
  • McIntyre, G.A., A method of unbiased selective sampling using ranked sets, Australian Jour- nal of Agricultural Research. 3 (1952), 385-390.
  • Muttlak, H.A., Parameters estimation in a simple linear regression using ranked set sampling, Biometrical Journal. 37 (1995), 799-810.
  • Muttlak, H.A., Estimation of parameters in a multiple regression model using ranked set sampling, Information and Optimization Sciences. 17 (1996), 521-533.
  • Özdemir, Y.A, Investigation of Parameter Estimation in Linear Regression Models Using Ranked Set Sampling, Gazi Üniversitesi Fen Bilimleri Enstitüsü, unpublished PhD thesis, (2005).
  • Samawi, H.M., Ababneh, F.M., On regression analysis using ranked set sample, Journal of Statistical Research. 35 (2001), 93-105.
  • Stokes, L.S., Ranked set sampling with concomitant variables, Commun. Statist. Theor. Meth. A6 (1977), 1207-1211.
  • Current address : Department of Statistics, Faculty of Science and Arts,University of Gazi, Be¸sevler, 06500, Ankara, Turkey
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Yaprak Arzu Özdemir This is me

Alptekin Esin A. This is me

Publication Date February 1, 2007
Published in Issue Year 2007 Volume: 56 Issue: 1

Cite

APA Özdemir, Y. A., & Esin A., A. (2007). PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 56(1), 7-20. https://doi.org/10.1501/Commua1_0000000194
AMA Özdemir YA, Esin A. A. PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2007;56(1):7-20. doi:10.1501/Commua1_0000000194
Chicago Özdemir, Yaprak Arzu, and Alptekin Esin A. “PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56, no. 1 (February 2007): 7-20. https://doi.org/10.1501/Commua1_0000000194.
EndNote Özdemir YA, Esin A. A (February 1, 2007) PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56 1 7–20.
IEEE Y. A. Özdemir and A. Esin A., “PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 56, no. 1, pp. 7–20, 2007, doi: 10.1501/Commua1_0000000194.
ISNAD Özdemir, Yaprak Arzu - Esin A., Alptekin. “PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56/1 (February 2007), 7-20. https://doi.org/10.1501/Commua1_0000000194.
JAMA Özdemir YA, Esin A. A. PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2007;56:7–20.
MLA Özdemir, Yaprak Arzu and Alptekin Esin A. “PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 56, no. 1, 2007, pp. 7-20, doi:10.1501/Commua1_0000000194.
Vancouver Özdemir YA, Esin A. A. PARAMETER ESTIMATION IN MULTIPLE LINEAR REGRESSION MODELS USING RANKED SET SAMPLING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2007;56(1):7-20.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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