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.
Similar content being viewed by others
Notes
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
Al-Saleh MF, Al-Omari AI (2002) Multistage ranked set sampling. J Stat Plan Inference 102:273–286
Al-Saleh MF, Samuh MJ (2008) On multistage ranked set sampling for distribution and median estimation. Comput Stat Data Anal 52:2066–2078
Bowley AL (1920) Elements of statistics. Charles Scribner’s Sons, New York
Chen Z (2007) Ranked set sampling: its essence and some new applications. Environ Ecol Stat 14:355–363
Chen Z, Bai Z, Sinha BK (2004) Ranked set sampling: theory and applications. Springer, New York
Chen H, Stasny EA, Wolfe DA (2005) Ranked set sampling for efficient estimation of a population proportion. Stat Med 24:3319–3329
Drikvandi R, Modarres R, Jalilian AH (2011) A bootstrap test for symmetry based on ranked set samples. Comput Stat Data Anal 55:1807–1814
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
Kvam PH (2003) Ranked set sampling based on binary water quality data with covariates. J Agric, Biol, Environ Stat 8:271–279
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
Ozturk O (2001) A nonparametric test of symmetry versus asymmetry for ranked-set samples. Commun Stat 30:2117–2133
Ozturk O (2002) Ranked set sample inference under a symmetry restriction. J Stat Plan Inference 102:317–336
Penrose KW, Nelson AG, Fisher AG (1985) Generalized body composition prediction equation for men using simple measurement techniques. Med Sci Sports Exerc 17:189
Schuster EF (1975) Estimating the distribution function of a symmetric distribution. Biometrika 62:631–635
Stokes SL (1977) Ranked set sampling with concomitant variables. Commun Stat 6:1207–1211
Stokes SL, Sager TW (1988) Characterizations of a ranked-set sample with application to estimating distribution functions. J Am Stat Assoc 83:374–381
Wolfe DA (2012) Ranked set sampling: its relevance and impact on statistical inference. ISRN Probab Stat, pp 1–32. Article ID 568385
Acknowledgements
The authors would like to thank two anonymous referees for their constructive comments that led to improvements in the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-017-0965-x