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Pitman closeness results concerning ranked set sampling


  • Jafari Jozani, Mohammad
  • Davies, Katherine F.
  • Balakrishnan, Narayanaswamy


We first compare the ranked set sampling (RSS) and simple random sampling schemes for the estimation of the population median through Pitman’s measure of closeness. Then, by using Banks’ criterion, we determine the frequency with which an individual order statistic is closer to the median than some symmetric estimator in an ϵ-neighbourhood of the median. Finally, we consider the simultaneous Pitman closeness criterion and identify the median RSS as the optimal RSS scheme for estimating the population median.

Suggested Citation

  • Jafari Jozani, Mohammad & Davies, Katherine F. & Balakrishnan, Narayanaswamy, 2012. "Pitman closeness results concerning ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2260-2269.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2260-2269 DOI: 10.1016/j.spl.2012.08.011

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    References listed on IDEAS

    1. Girard, Stéphane & Jacob, Pierre, 2008. "Frontier estimation via kernel regression on high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 403-420, March.
    2. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729.
    3. Deyuan Li & Liang Peng & Yongcheng Qi, 2011. "Empirical likelihood confidence intervals for the endpoint of a distribution function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 353-366, August.
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    Cited by:

    1. Tie Ma & Shuangzhe Liu, 2014. "Pitman closeness of the class of isotonic estimators for ordered scale parameters of two Gamma distributions," Statistical Papers, Springer, vol. 55(3), pages 615-625, August.


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