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Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable

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Abstract

The estimation of the means of the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) is considered. The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered. The estimators obtained are compared to their counterparts based on simple random sampling (SRS). It appears that the suggested estimators are more efficient. Also, MERSS with concomitant variable is easier to use in practice than the usual ranked set sampling (RSS) with concomitant variable. The issue of robustness of the procedure is addressed. Real trees data set is used for illustration.

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References

  1. Al-Hadhrami, S. (2001). Parametric estimation using moving extreme ranked set sampling. Master thesis, Sultan Qaboos University, Oman.

    Google Scholar 

  2. Al-Odat, M. T. and Al-Saleh, M. F. (2001). A variation of ranked set sampling. Journal of Applied Statistical Science 10, 137–246.

    MathSciNet  Google Scholar 

  3. Al-Saleh, M. F. (2004). Steady state ranked set sampling and parametric estimation. Journal of Statistical Planning and Inference 123(1), 83–95.

    Article  MATH  MathSciNet  Google Scholar 

  4. Al-Saleh, M. F. and Al-Hadhrami, S. (2003a). Parametric estimation for the location parameter for symmetric distribution using moving extreme ranked set sampling with application to trees data. Environmetrics 14(7), 651–664.

    Article  Google Scholar 

  5. Al-Selah, M. F. and Al-Hadhrami, S. (2003b). Estimation of the mean of the exponential distribution using moving extreme ranked set sampling. Statistical Papers 44, 367–382.

    Article  MathSciNet  Google Scholar 

  6. Al-Saleh, M. F. and Al-Shrafat, K. (2001). Estimation average milk yield using RSS. Environmetrics 12, 395–399.

    Article  Google Scholar 

  7. Al-Saleh, M. F. and Zheng, G. (2002). Estimation of bivariate characteristics using ranked set sampling. The Australian and New Zealand Journal of Statistics 44 221–232.

    Article  MATH  MathSciNet  Google Scholar 

  8. Al-Saleh, M. F. (1994). Mill's Ratio-A Bayesian approach. Pakistan Journal of Statistics 10, 629–632.

    MATH  MathSciNet  Google Scholar 

  9. Arnold, B., Balakrishnan, N. and Nagaraja, H. (1992). A first course in order statistics. John Wiley and Sons, New York.

    MATH  Google Scholar 

  10. Halls, L. and Dell, T. (1966). Trials of ranked set sampling for forage yields. Forest Science 12, 22–26.

    Google Scholar 

  11. Kaur, A., Patil, G.P., Sinha, A.K. and Taillie, C. (1995). Ranked set sampling: An annotated bibliography. Environmental and Ecological Statistics 2, 25–54.

    Article  Google Scholar 

  12. Lehmann, E. (1983). Theory of point estimation. John Wiley and Sons, New York.

    MATH  Google Scholar 

  13. Lehmann, E. (1966). Some concepts of dependence. Annals of Mathematical Statistics 37, 1137–1153.

    MathSciNet  MATH  Google Scholar 

  14. Lindsey, J. (1999). Multivariate elliptically contoured distributions for repeated measurements. Biometrics 55, 1277–1280.

    Article  MATH  Google Scholar 

  15. Barabesi, L. and Pisani, C. (2004). Steady-state ranked set sampling for replicated environmental sampling designs. Environmetrics 15, 45–56.

    Article  Google Scholar 

  16. Martin, W., T. Oderwald, R. and Smith, D. (1980). Evaluation of RSS for estimating shrub phytomass in appalacachian oak forest. School of Forest and Wildlife Resources, Virginia Polytechnic Institute and State University.

  17. McIntyre, G. (1952). A method for unbiased selective sampling using ranked set sampling. Australian Journal of Agricultural Research 3, 385–390.

    Article  Google Scholar 

  18. Mehrotra, K. and Nanda, P. (1974). Unbiased estimation of parameters by order statistics in the case of censored samples. Biometrika 61, 601–606.

    Article  MATH  MathSciNet  Google Scholar 

  19. Mode, N. Conquest, L. and Marker, D. (1999). Ranked set sampling for ecological research: accounting for the total cost of sampling. Environmetrics 10, 179–194.

    Article  Google Scholar 

  20. Nahhas, R., Wolf, D. and Chen, H. (2004). Ranked set sampling: Ranking error models and estimation of visual judgment error variance. Biometrical Journal 46, 255–263.

    Article  Google Scholar 

  21. Patil, G., Sinha, A., and Taillie, C. (1994). Ranked set sampling for multiple characteristics. International Journal for Ecology and Environmental Sciences 20, 357–373.

    Google Scholar 

  22. Patil, G., Sinha, A., and Taillie, C. (1999). Ranked set sampling: Bibliography. Environmental and Ecological Statistics 6, 91–98.

    Article  Google Scholar 

  23. Prodan, M. (1968). Forest Biometrics. Program Press, London.

    Google Scholar 

  24. Samawi, H. and Al-Saleh, M. F. (2004). On bivariate ranked set sampling for quantile estimation and quantile interval estimation using ratio estimator. Communications in Statistics-Theory and Methods 33, 1801–20.

    Article  MATH  MathSciNet  Google Scholar 

  25. Samawi, H., Ahmad, M. and Abu-Dayyeh, W. (1996). Estimating the population mean using extreme ranked set sampling. Biometrical Journal 30, 577–586.

    Google Scholar 

  26. Stokes, S. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods 6, 1207–1211.

    Google Scholar 

  27. Stokes, S. (1980). Inferences on the correlation coefficient in bivariate normal populations from ranked set samples. Journal of the American Statistical Association 75, 989–995.

    Article  MATH  MathSciNet  Google Scholar 

  28. Takahasi, K. 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.

    Article  MATH  MathSciNet  Google Scholar 

  29. Yang, S. (1977). General distribution theory of the concomitants of order statistics. Annals of Statistics 5, 996–1002.

    MATH  MathSciNet  Google Scholar 

  30. Zheng, G. and Al-Saleh, M. F. (2002). Modified maximum likelihood estimator based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54 641–6.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Yarmouk University, Irbid, Jordan

    Mohammad Fraiwan Al-Saleh & Ahmad Mohammad Al-Ananbeh

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  1. Mohammad Fraiwan Al-Saleh
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  2. Ahmad Mohammad Al-Ananbeh
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Al-Saleh, M.F., Al-Ananbeh, A.M. Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable. Statistical Papers 48, 179–195 (2007). https://doi.org/10.1007/s00362-006-0325-8

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  • DOI: https://doi.org/10.1007/s00362-006-0325-8

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