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Abstract
Regression is used to estimate the population mean of the response variable, , in the two cases where the population mean of the concomitant (auxiliary) variable, , is known and where it is unknown. In the latter case, a double sampling method is used to estimate the population mean of the concomitant variable. We invesitagate the performance of the two methods using extreme ranked set sampling (ERSS), as discussed by Samawi et al. (1996). Theoretical and Monte Carlo evaluation results as well as an illustration using actual data are presented. The results show that if the underlying joint distribution of and is symmetric, then using ERSS to obtain regression estimates is more efficient than using ranked set sampling (RSS) or simple random sampling (SRS).
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References
- HEDAYAT, A.S. and SINHA, B.K. 1992. Design and inference in finite population sampling. New York: Wiley.
- KAUR, A., PATIL, G.P., SINHA A.K. and TAILLIE, C. 1995. Ranked set sampling: An annotated bibliography. Environmental and Ecological Statistics 2: 25-53
- JOHNSON, M.E. 1987. Multivariate Statistical Simulation. New York: Wiley.
- MCINTYRE, G.A., 1952. A method of unbiased selective sampling, using ranked sets. Australian J. Agricultural Research 3: 385-390.
- NELSON, W.E. BEHRMAN, R.E., KLIEGMAN, R.M. and VANGHAN, V.C. 1994. Textbook of pediatrics. 4th edn. W. B. Saunders Company Harcourt Barance Jovanovich, Inc.
- PATIL, G.P., SINHA, A.K. and TAILLIE 1999. Ranked set sampling: a bibliography. Environmental and Ecological Statistics. 6 (1): 91-98.
- PATIL, G.P., SINHA, A.K. and TAILLIE 1993. Relative precision of ranked set sampling: Comparison with regression estimator. Environmetrics. 4 (4): 399-412.
- SAMAWI, H.M. and Al-SAGHEER, O.A. 2001. On the estimation of the distribution function using extreme and median ranked set sampling. Biom. J. 43 (3): 357-373.
- SAMAWI, H.M., MOHMMAD, S. and ABU-DAYYEH, W. 1996. Estimating the population means using extreme ranked set sampling. Biom. Journal. 38: 577-586.
- SUKHATME. P.V. and SUKHATME, B.V. 1970. Sampling Theory of Surveys with Applications. Ames: Iowa State University Press.
- TIKKIWAL. B.D. 1960. On the theory of classical regression and double sampling estimation. Journal of the Royal Statistical Society, Series B 22: 131-138.
- YANAGAWA, T. and CHEN, S.H. 1980. The MG procedure in ranked set sampling: Comparision with the regression estimator.
- YU, P.L.H. and LAM, K. 1997. Regression estimator in rank set sampling. Biometrics, 53: 1070-1080.
References
HEDAYAT, A.S. and SINHA, B.K. 1992. Design and inference in finite population sampling. New York: Wiley.
KAUR, A., PATIL, G.P., SINHA A.K. and TAILLIE, C. 1995. Ranked set sampling: An annotated bibliography. Environmental and Ecological Statistics 2: 25-53
JOHNSON, M.E. 1987. Multivariate Statistical Simulation. New York: Wiley.
MCINTYRE, G.A., 1952. A method of unbiased selective sampling, using ranked sets. Australian J. Agricultural Research 3: 385-390.
NELSON, W.E. BEHRMAN, R.E., KLIEGMAN, R.M. and VANGHAN, V.C. 1994. Textbook of pediatrics. 4th edn. W. B. Saunders Company Harcourt Barance Jovanovich, Inc.
PATIL, G.P., SINHA, A.K. and TAILLIE 1999. Ranked set sampling: a bibliography. Environmental and Ecological Statistics. 6 (1): 91-98.
PATIL, G.P., SINHA, A.K. and TAILLIE 1993. Relative precision of ranked set sampling: Comparison with regression estimator. Environmetrics. 4 (4): 399-412.
SAMAWI, H.M. and Al-SAGHEER, O.A. 2001. On the estimation of the distribution function using extreme and median ranked set sampling. Biom. J. 43 (3): 357-373.
SAMAWI, H.M., MOHMMAD, S. and ABU-DAYYEH, W. 1996. Estimating the population means using extreme ranked set sampling. Biom. Journal. 38: 577-586.
SUKHATME. P.V. and SUKHATME, B.V. 1970. Sampling Theory of Surveys with Applications. Ames: Iowa State University Press.
TIKKIWAL. B.D. 1960. On the theory of classical regression and double sampling estimation. Journal of the Royal Statistical Society, Series B 22: 131-138.
YANAGAWA, T. and CHEN, S.H. 1980. The MG procedure in ranked set sampling: Comparision with the regression estimator.
YU, P.L.H. and LAM, K. 1997. Regression estimator in rank set sampling. Biometrics, 53: 1070-1080.