Environmental and Ecological Statistics

, Volume 18, Issue 4, pp 757–779 | Cite as

Sampling from partially rank-ordered sets

  • Omer Ozturk


In this paper we introduce a new sampling design. The proposed design is similar to a ranked set sampling (RSS) design with a clear difference that rankers are allowed to declare any two or more units are tied in ranks whenever the units can not be ranked with high confidence. These units are replaced in judgment subsets. The fully measured units are then selected from these partially ordered judgment subsets. Based on this sampling scheme, we develop unbiased estimators for the population mean and variance. We show that the proposed sampling procedure has some advantages over standard ranked set sampling.


Ranked set sampling Imperfect ranking Sampling design Observational economy Variance estimation 


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  1. Chen Z, Bai ZD, Sinha KB (2004) Ranked set sampling: theory and application, lecture notes in Statistics 176. Springer, New YorkGoogle Scholar
  2. Dell TR, Clutter JL (1972) Ranked-set sampling theory with order statistics background. Biometrics 28: 545–555CrossRefGoogle Scholar
  3. Frey J (2007) New imperfect ranking models for ranked set sampling. J Stat Plan Inference 137: 1433–1445CrossRefGoogle Scholar
  4. Fligner M, MacEachern SN (2006) Ranked set sampling: models and distribution free two sample methods under imperfect ranking. J Am Stat Assoc 475: 1107–1118CrossRefGoogle Scholar
  5. Kaur A, Patil GP, Taillie C (1997) Unequal allocation models for ranked set sampling with skew distributions. Biometrics 53: 123–137CrossRefGoogle Scholar
  6. MacEachern SN, Ozturk O, Stark G, Wolfe DA (2002) A new ranked set sample estimator of variance. J R Stat Soc Series B 64: 177–188CrossRefGoogle Scholar
  7. McIntyre GA (1952) A method for unbiased selective sampling, using ranked-sets. Aust J Agric Res 3: 385–390CrossRefGoogle Scholar
  8. McIntyre GA (2005) A method of unbiased selective sampling using ranked sets. Am Stat 3: 230–232CrossRefGoogle Scholar
  9. Ozturk O, MacEachern SN (2007) Order restricted randomized designs and two sample inference. Environ Ecol Stat 14: 365–381CrossRefGoogle Scholar
  10. Perron F, Sinha BK (2004) Estimation of variance based on ranked set sample. J Stat Plan Inference 120: 21–28CrossRefGoogle Scholar
  11. Stokes SL (1980) Estimation of variance using judgment ordered ranked set samples. Biometrics 36: 35–42CrossRefGoogle Scholar
  12. Stokes SL, Sager TW (1988) Characterization of a ranked-set sample with application to estimating distribution functions. J Am Stat Assoc 83: 374–381CrossRefGoogle Scholar
  13. Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20: 1–31CrossRefGoogle Scholar
  14. Wang X, Lim J, Stokes L (2008) A nonparametric mean estimator for judgment post stratified data. Biometrics 64: 355–363PubMedCrossRefGoogle Scholar
  15. Wang X, Stokes L, Lim J, Chen M (2006) Concomitants of multivariate order statistics with application to judgment poststratification. J Am Stat Assoc 101: 1693–1704CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA

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