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Estimation of a symmetric distribution function in multistage ranked set sampling

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Abstract

This article concerns estimation of a symmetric distribution function under multistage ranked set sampling. A nonparametric estimator is developed and its theoretical properties are explored. Performance of the suggested estimator is further evaluated using numerical studies.

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Notes

  1. The data set can be found at http://lib.stat.cmu.edu/datasets/bodyfat.

References

  • Al-Saleh MF, Al-Kadiri M (2000) Double-ranked set sampling. Stat Prob Lett 48:205–212

    Article  MathSciNet  Google Scholar 

  • Al-Saleh MF, Al-Omari AI (2002) Multistage ranked set sampling. J Stat Plan Inference 102:273–286

    Article  MathSciNet  Google Scholar 

  • Al-Saleh MF, Samuh MJ (2008) On multistage ranked set sampling for distribution and median estimation. Comput Stat Data Anal 52:2066–2078

    Article  MathSciNet  Google Scholar 

  • Bowley AL (1920) Elements of statistics. Charles Scribner’s Sons, New York

    MATH  Google Scholar 

  • Chen Z (2007) Ranked set sampling: its essence and some new applications. Environ Ecol Stat 14:355–363

    Article  MathSciNet  Google Scholar 

  • Chen Z, Bai Z, Sinha BK (2004) Ranked set sampling: theory and applications. Springer, New York

    Book  Google Scholar 

  • Chen H, Stasny EA, Wolfe DA (2005) Ranked set sampling for efficient estimation of a population proportion. Stat Med 24:3319–3329

    Article  MathSciNet  Google Scholar 

  • Drikvandi R, Modarres R, Jalilian AH (2011) A bootstrap test for symmetry based on ranked set samples. Comput Stat Data Anal 55:1807–1814

    Article  MathSciNet  Google Scholar 

  • Frey J, Feeman TG (2016) Efficiency comparisons for partially rank-ordered set sampling. Stat Pap. https://doi.org/10.1007/s00362-016-0742-2

  • Kadilar C, Unyazici Y, Cingi H (2009) Ratio estimator for the population mean using ranked set sampling. Stat Pap 50:301–309

    Article  MathSciNet  Google Scholar 

  • Kvam PH (2003) Ranked set sampling based on binary water quality data with covariates. J Agric, Biol, Environ Stat 8:271–279

    Article  Google Scholar 

  • Mahdizadeh M, Zamanzade E (2016) A new reliability measure in ranked set sampling. Stat Pap. https://doi.org/10.1007/s00362-016-0794-3

  • McIntyre GA (1952) A method of unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research 3:385–390

    Article  Google Scholar 

  • Ozturk O (2001) A nonparametric test of symmetry versus asymmetry for ranked-set samples. Commun Stat 30:2117–2133

    Article  MathSciNet  Google Scholar 

  • Ozturk O (2002) Ranked set sample inference under a symmetry restriction. J Stat Plan Inference 102:317–336

    Article  MathSciNet  Google Scholar 

  • Penrose KW, Nelson AG, Fisher AG (1985) Generalized body composition prediction equation for men using simple measurement techniques. Med Sci Sports Exerc 17:189

    Article  Google Scholar 

  • Schuster EF (1975) Estimating the distribution function of a symmetric distribution. Biometrika 62:631–635

    Article  MathSciNet  Google Scholar 

  • Stokes SL (1977) Ranked set sampling with concomitant variables. Commun Stat 6:1207–1211

    Article  Google Scholar 

  • Stokes SL, Sager TW (1988) Characterizations of a ranked-set sample with application to estimating distribution functions. J Am Stat Assoc 83:374–381

    Article  MathSciNet  Google Scholar 

  • Wolfe DA (2012) Ranked set sampling: its relevance and impact on statistical inference. ISRN Probab Stat, pp 1–32. Article ID 568385

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Acknowledgements

The authors would like to thank two anonymous referees for their constructive comments that led to improvements in the paper.

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Correspondence to M. Mahdizadeh.

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Mahdizadeh, M., Zamanzade, E. Estimation of a symmetric distribution function in multistage ranked set sampling. Stat Papers 61, 851–867 (2020). https://doi.org/10.1007/s00362-017-0965-x

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  • DOI: https://doi.org/10.1007/s00362-017-0965-x

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