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Using ranked set sampling with extreme ranks in estimating the population proportion.

Ehsan Zamanzade1, M Mahdizadeh2

  • 1Department of Statistics, University of Isfahan, Isfahan, Iran.

Statistical Methods in Medical Research
|February 2, 2019
PubMed
Summary

This study introduces a more efficient maximum likelihood estimator for population proportions using ranked set sampling with extreme ranks. This new method outperforms traditional techniques, especially for extreme proportion values.

Keywords:
Cost efficiencyjudgment rankingpopulation proportionranked set samplingrelative efficiency

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Area of Science:

  • Statistics
  • Statistical Inference

Background:

  • Estimating population proportion is crucial in statistical analysis.
  • Ranked set sampling (RSS) offers potential efficiency gains over simple random sampling (SRS).
  • Extreme ranks in RSS may further enhance estimation properties.

Purpose of the Study:

  • To investigate the properties of the maximum likelihood estimator (MLE) for population proportion under ranked set sampling with extreme ranks.
  • To compare the efficiency of this proposed estimator against SRS and standard RSS analogs.

Main Methods:

  • Derivation of the maximum likelihood estimator for population proportion in extreme rank RSS.
  • Asymptotic distribution analysis of the proposed estimator.
  • Monte Carlo simulation studies to evaluate finite sample performance.

Main Results:

  • The proposed MLE demonstrates superior efficiency compared to SRS and standard RSS estimators.
  • Efficiency gains are particularly pronounced when the true population proportion approaches zero or one.
  • The estimator's properties are validated through simulation studies.

Conclusions:

  • The maximum likelihood estimator in ranked set sampling with extreme ranks provides a more efficient method for estimating population proportions.
  • This method offers significant advantages over traditional sampling techniques, especially in scenarios with extreme population proportions.
  • The findings have practical implications for survey data analysis, as demonstrated by the National Health and Nutrition Examination Survey example.