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Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering

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  • Vic Barnett
  • Karen Moore

Abstract

Ranked-set sampling is a widely used sampling procedure when sample observations are expensive or difficult to obtain. It departs from simple random sampling by seeking to spread the observations in the sample widely over the distribution or population. This is achieved by ranking methods which may need to employ concomitant information. The ranked-set sample mean is known to be more efficient than the corresponding simple random sample mean. Instead of the ranked-set sample mean, this paper considers the corresponding optimal estimator: the ranked-set best linear unbiased estimator. This is shown to be more efficient, even for normal data, but particularly for skew data, such as from an exponential distribution. The corresponding forms of the estimators are quite distinct from the ranked-set sample mean. Improvement holds where the ordering is perfect or imperfect, with this prospect of improper ordering being explored through the use of concomitants. In addition, the corresponding optimal linear estimator of a scale parameter is also discussed. The results are applied to a biological problem that involves the estimation of root weights for experimental plants, where the expense of measurement implies the need to minimize the number of observations taken.

Suggested Citation

  • Vic Barnett & Karen Moore, 1997. "Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 697-710.
    • Handle: RePEc:taf:japsta:v:24:y:1997:i:6:p:697-710
    DOI: 10.1080/02664769723431
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    References listed on IDEAS

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    1. Sinha Bimal K. & Sinha Bikas K. & Purkayastha Sumitra, 1996. "On Some Aspects Of Ranked Set Sampling For Estimation Of Normal And Exponential Parameters," Statistics & Risk Modeling, De Gruyter, vol. 14(3), pages 223-240, March.
    2. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    3. M. S. Ridout & J. M. Cobby, 1987. "Ranked Set Sampling with Non‐Random Selection of Sets and Errors in Ranking," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 145-152, June.
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    Cited by:

    1. Wang, You-Gan & Zhu, Min, 2005. "Optimal sign tests for data from ranked set samples," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 13-22, April.
    2. Gang Zheng & Mohammad Al-Saleh, 2003. "Improving the best linear unbiased estimator for the scale parameter of symmetric distributions by using the absolute value of ranked set samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 253-265.
    3. Ramzi W. Nahhas & Douglas A. Wolfe & Haiying Chen, 2002. "Ranked Set Sampling: Cost and Optimal Set Size," Biometrics, The International Biometric Society, vol. 58(4), pages 964-971, December.
    4. Manoj Chacko & P. Thomas, 2008. "Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 301-318, June.
    5. Manoj Chacko, 2017. "Bayesian estimation based on ranked set sample from Morgenstern type bivariate exponential distribution when ranking is imperfect," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 333-349, April.
    6. Raqab, Mohammad Z. & Kouider, Elies & Al-Shboul, Qasim M., 2002. "Best linear invariant estimators using ranked set sampling procedure: comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 97-105, March.
    7. Vic Barnett & Maria Cecilia Mendes Barreto, 2001. "Estimators for a Poisson parameter using ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 929-941.
    8. Jesse Frey & Omer Ozturk, 2011. "Constrained estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 769-789, August.

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