Abstract
When sample observations are expensive or difficult to obtain, ranked set sampling is known to be an efficient method for estimating the population mean, and in particular to improve on the sample mean estimator. Using best linear unbiased estimators, this paper considers the simple linear regression model with replicated observations. Use of a form of ranked set sampling is shown to be markedly more efficient for normal data when compared with the traditional simple linear regression estimators.
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Arnold, B. and Balakrishnan, N. (1989) Relations, Bounds and Approximations for Order Statistics, Springer-Verlag, New York.
Balakrishnan, N. (1986) Order statistics from discrete distributions. Communications in Statistics, Part A—Theory and Methods, 15, 657-75.
Balakrishnan, N. and Cohen, C. (1991) Order Statistics and Inference: Estimation Methods, Academic Press, San Diego.
Barnett, V. and Moore, K. (1997) Best linear unbiased estimates in ranked set sampling with particular reference to imperfect ordering. Journal of Applied Statistics, 24, 697-710.
Bhoj, D.S. and Ahsanullah, M. (1996) Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52, 685-94.
Bohn, L.L. (1996) A review of nonparametric ranked set sampling methodology. Communications in Statistics, Part A—Theory and Methods, 25, 2675-85.
Bohn, L.L. and Wolfe, D.A. (1992) Nonparametric 2 sample procedures for ranked set samples data. Journal of the American Statistical Association, 87, 552-62.
Bohn, L.L. and Wolfe, D.A. (1994) The effect of imperfect judgment rankings on properties of procedures based on the ranked set samples analog of the Mann-Whitney-Wilcoxon statistics. Journal of the American Statistical Association, 89, 168-76.
David, H.A. (1981) Order Statistics, 2nd ed., John Wiley, New York.
Gupta, S.S. and Panchapakesan, P. (1974) On moments of order statistics from independent binomial populations. Annals of the Institute of Statistical Mathematics, 8, 95-113.
Dell, T.R. and Clutter, J.L. (1972) Ranked set sampling theory with the use of ranked set sampling on grass clover swards. Grass and Forage Science, 40, 257-63.
Johnson, N., Kotz, S., and Kemp, A. (1992) Univariate Discrete Distributions, 2nd ed., John Wiley, New York.
Kaur, A., Patil, G.P., Shirk, S.J., and Taillie, C. (1996) Environmental sampling with a concomitant variable and stratified simple random sampling. Journal of Applied Statistics, 23, 231-55.
Kendall, M.G. and Stuart, A. (1979) The Advanced Theory of Statistics, Volume 1: Inference and Relationship, 4th ed., Griffin, London.
Koti, K.M. and Babu, G.J. (1996) Sign test for ranked set sampling. Communications in Statistics, Part A—Theory and Methods, 25, 1617-30.
Kvam, P.H. and Samaniego, F.J. (1994) Nonparametric maximum-likelihood-estimation based on ranked set samples. Journal of the American Statistical Association, 89, 526-37.
Lam, K., Sinha, B.K., and Wu, Z. (1994) Estimation of parameters in a 2-parameter exponential-distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723-36.
Lloyd, E.H. (1952) Generalized least-squares theorem. In Contributions to order statistics, A.E. Sarhan and B.G. Greenberg (eds)., (1992) John Wiley, New York, pp. 20-7.
McIntyre, G.A. (1952) A method of unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3, 385-90.
Muttlak, H.A. (1995) Parameters estimation in a simple linear-regression using rank set sampling. Biometrical Journal, 37, 799-810.
Muttlak, H.A. (1996) Estimation of parameters for one-way layout with rank set sampling. Biometrical Journal, 38, 507-15.
Muttlak, H.A. and McDonald, L.L. (1990) Ranked set sampling with respect to concomitant variables and with size biased probability of selection. Communications in Statistics, Part A—Theory and Methods, 19, 653-67.
Muttlak, H.A. and McDonald, L.L. (1992) Ranked set sampling and the line intercept method—a more efficient procedure. Biometrical Journal, 34, 329-46.
Pearson, E.S. and Hartley, H.O. (1976) Biometrika Tables for Statisticians, vol. 2, Griffin, London.
Ridout, M.S. and Cobby, J.M. (1987) Ranked set sampling with non-random selection of sets and errors in ranking. Applied Statistics, 36, 145-52.
Samawi, H.M., Ahmed, M.S., and Abudayyeh, W. (1996) Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38, 577-86.
Sinha, Bimal.K., Sinha, Bikas.K., and Purkayastha, S. (1996) On some aspects of ranked set sampling for estimation of normal and exponential parameters. Statistical Decisions, 14, 223-40.
Stokes, L.S. (1977) Ranked set sampling with concomitant variables. Communications in Statistics, Part A—Theory and Methods, 25, 1617-30.
Stokes, L.S. (1980) Estimation of variance using judgement ordered ranked set samples. Biometrics, 36, 35-42.
Stokes, S.L. (1995) Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47, 465-82.
Stokes, S.L. and Sager, T.W. (1988) Characterization of a ranked set sample with application to estimating distributions functions. Journal of the American Statistical Association, 83, 374-81.
Takahasi, K. and Wakimoto, K. (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 20, 1-31.
Yu, P.L.H. and Lam, K. (1997) Regression estimator in ranked set sampling. Biometrics, 53, 1070-80.
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Barreto, M.C.M., Barnett, V. Best linear unbiased estimators for the simple linear regression model using ranked set sampling. Environmental and Ecological Statistics 6, 119–133 (1999). https://doi.org/10.1023/A:1009609902784
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DOI: https://doi.org/10.1023/A:1009609902784