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Proportion estimation in ranked set sampling in the presence of tie information

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  • Ehsan Zamanzade

    (University of Isfahan)

  • Xinlei Wang

    (Southern Methodist University)

Abstract

Ranked set sampling (RSS) is a statistical technique that uses auxiliary ranking information of unmeasured sample units in an attempt to select a more representative sample that provides better estimation of population parameters than simple random sampling. However, the use of RSS can be hampered by the fact that a complete ranking of units in each set must be specified when implementing RSS. Recently, to allow ties declared as needed, Frey (Environ Ecol Stat 19(3):309–326, 2012) proposed a modification of RSS, which is to simply break ties at random so that a standard ranked set sample is obtained, and meanwhile record the tie structure for use in estimation. Under this RSS variation, several mean estimators were developed and their performance was compared via simulation, with focus on continuous outcome variables. We extend the work of Frey (2012) to binary outcomes and investigate three nonparametric and three likelihood-based proportion estimators (with/without utilizing tie information), among which four are directly extended from existing estimators and the other two are novel. Under different tie-generating mechanisms, we compare the performance of these estimators and draw conclusions based on both simulation and a data example about breast cancer prevalence. Suggestions are made about the choice of the proportion estimator in general.

Suggested Citation

  • Ehsan Zamanzade & Xinlei Wang, 2018. "Proportion estimation in ranked set sampling in the presence of tie information," Computational Statistics, Springer, vol. 33(3), pages 1349-1366, September.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-018-0807-x
    DOI: 10.1007/s00180-018-0807-x
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    References listed on IDEAS

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    1. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    2. Steven N. MacEachern & Elizabeth A. Stasny & Douglas A. Wolfe, 2004. "Judgement Post-Stratification with Imprecise Rankings," Biometrics, The International Biometric Society, vol. 60(1), pages 207-215, March.
    3. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, October.
    4. Mu, Xiaosheng, 2015. "Log-concavity of a mixture of beta distributions," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 125-130.
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    Cited by:

    1. Shashi Bhushan & Anoop Kumar & Sana Shahab & Showkat Ahmad Lone & Salemah A. Almutlak, 2022. "Modified Class of Estimators Using Ranked Set Sampling," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    2. Shashi Bhushan & Anoop Kumar & Amer Ibrahim Al-Omari & Ghadah A. Alomani, 2023. "Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    3. Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.

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