Advertisement

Computational Statistics

, Volume 33, Issue 3, pp 1325–1348 | Cite as

Interval estimation of \(P(X<Y)\) in ranked set sampling

  • M. Mahdizadeh
  • Ehsan Zamanzade
Original Paper
  • 189 Downloads

Abstract

This article deals with constructing a confidence interval for the reliability parameter using ranked set sampling. Some asymptotic and resampling-based intervals are suggested, and compared with their simple random sampling counterparts using Monte Carlo simulations. Finally, the methods are applied on a real data set in the context of agriculture.

Keywords

Bootstrap Jackknife Judgment ranking 

Notes

Acknowledgements

This research was supported by Iran National Science Foundation (INSF). The authors wish to thank the reviewers for insightful comments and suggestions that improved an earlier version of this paper.

Supplementary material

180_2018_795_MOESM1_ESM.pdf (72 kb)
Supplementary material 1 (pdf 72 KB)

References

  1. Ayech MW, Ziou D (2015) Segmentation of Terahertz imaging using \(k\)-means clustering based on ranked set sampling. Expert Syst Appl 42:2959–2974CrossRefGoogle Scholar
  2. Chen Z (1999) Density estimation using ranked-set sampling data. Environ Ecol Stat 6:135–146CrossRefGoogle Scholar
  3. Chen Z (2007) Ranked set sampling: its essence and some new applications. Environ Ecol Stat 14:355–363MathSciNetCrossRefGoogle Scholar
  4. Chen Z, Bai Z, Sinha BK (2004) Ranked set sampling: theory and applications. Springer, New YorkCrossRefzbMATHGoogle Scholar
  5. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26MathSciNetCrossRefzbMATHGoogle Scholar
  6. Halls LK, Dell TR (1966) Trial of ranked-set sampling for forage yields. For Sci 12:22–26Google Scholar
  7. Hollander M, Wolfe DA, Chicken E (2014) Nonparametric statistical methods, 3rd edn. Wiley, New YorkzbMATHGoogle Scholar
  8. Howard RW, Jones SC, Mauldin JK, Beal RH (1982) Abundance, distribution, and colony size estimates for Reticulitermes spp. (Isoptera: Rhinotermitidae) in Southern Mississippi. Environ Entomol 11:1290–1293CrossRefGoogle Scholar
  9. Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations. Theory and applications. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  10. Kvam P (2003) Ranked set sampling based on binary water quality data with covariates. J Agric Biol Environ Stat 8:271–279CrossRefGoogle Scholar
  11. MacEachern SN, Ozturk O, Stark GV, Wolfe DA (2002) A new ranked set sample estimator of variance. J R Stat Soc Ser B 64:177–188MathSciNetCrossRefzbMATHGoogle Scholar
  12. Mahdizadeh M, Zamanzade E (2016) Kernel-based estimation of \(P(X>Y)\) in ranked set sampling. SORT 40:243–266MathSciNetzbMATHGoogle Scholar
  13. McIntyre GA (1952) A method of unbiased selective sampling using ranked sets. Aust J Agric Res 3:385–390CrossRefGoogle Scholar
  14. Modarres R, Hui TP, Zheng G (2006) Resampling methods for ranked set samples. Comput Stat Data Anal 51:1039–1050MathSciNetCrossRefzbMATHGoogle Scholar
  15. Murray RA, Ridout MS, Cross JV (2000) The use of ranked set sampling in spray deposit assessment. Asp Appl Biol 57:141–146Google Scholar
  16. Presnell B, Bohn L (1999) U-statistics and imperfect ranking in ranked set sampling. J Nonparametr Stat 10:111–126MathSciNetCrossRefzbMATHGoogle Scholar
  17. Quenouille MH (1956) Notes on bias in estimation. Biometrika 43:353–360MathSciNetCrossRefzbMATHGoogle Scholar
  18. Sengupta S, Mukhuti S (2008) Unbiased estimation of \(P(X>Y)\) using ranked set sample data. Statistics 42:223–230MathSciNetCrossRefzbMATHGoogle Scholar
  19. Sheather SJ (2004) Density estimation. Stat Sci 19:588–597CrossRefzbMATHGoogle Scholar
  20. Stokes SL (1980) Estimation of variance using judgment ordered ranked set samples. Biometrics 36:35–42MathSciNetCrossRefzbMATHGoogle Scholar
  21. Terpstra J, Miller ZA (2006) Exact inference for a population proportion based on a ranked set sample. Commun Stat Simul Comput 35:19–26MathSciNetCrossRefzbMATHGoogle Scholar
  22. Tukey JW (1958) Bias and confidence in not quite large samples (abstract). Ann Math Stat 29:614CrossRefGoogle Scholar
  23. Wang JF, Stein A, Gao BB, Ge Y (2012) A review of spatial sampling. Spat Stat 2:1–14CrossRefGoogle Scholar
  24. Wolfe DA (2012) Ranked set sampling: its relevance and impact on statistical inference. ISRN Probability and Statistics, pp 1–32Google Scholar
  25. Yin J, Hao Y, Samawi H, Rochani H (2016) Rank-based kernel estimation of the area under the ROC curve. Stat Methodol 32:91–106MathSciNetCrossRefGoogle Scholar
  26. Zamanzade E, Mahdizadeh M (2017) A more efficient proportion estimator in ranked set sampling. Stat Probab Lett 129:28–33MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsHakim Sabzevari UniversitySabzevarIran
  2. 2.Department of StatisticsUniversity of IsfahanIsfahanIran

Personalised recommendations