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Computational Statistics

, Volume 33, Issue 3, pp 1349–1366 | Cite as

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

  • Ehsan Zamanzade
  • Xinlei Wang
Original Paper
  • 120 Downloads

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.

Keywords

Imperfect ranking Isotonic estimation Maximum likelihood Nonparametric estimation Ranking tie Relative efficiency 

Notes

Acknowledgements

We thank Professor Johan Lim for his comments on an earlier version of this paper, Professor Jesse Frey for sharing his R-Code and the UCI machine learning repository for online data use. We are also thankful to two anonymous referees and an associate editor for their valuable comments which improved an earlier version of this paper.

Compliance with ethical standards

Conflict of interest

No potential conflict of interest was reported by the authors.

Supplementary material

180_2018_807_MOESM1_ESM.pdf (497 kb)
Supplementary material 1 (pdf 496 KB)

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Copyright information

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

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of IsfahanIsfahanIran
  2. 2.Department of Statistical ScienceSouthern Methodist UniversityDallasUSA

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