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Efficient estimators with categorical ranked set samples: estimation procedures for osteoporosis.

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Ranked set sampling (RSS) offers a cost-effective approach for analyzing ordinal populations, especially when data measurement is expensive. This study introduces new estimators using RSS data with ties, improving parameter estimation for conditions like bone disorders.

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Area of Science:

  • Statistics
  • Biostatistics
  • Sampling Theory

Background:

  • Ranked set sampling (RSS) is a cost-effective sampling technique.
  • It is particularly useful when measuring the variable of interest is expensive or time-consuming.
  • Ranking information is often obtainable at low cost.

Purpose of the Study:

  • To analyze ordinal population data using Ranked set sampling (RSS).
  • To compare the issue of non-representative extreme samples between RSS and simple random sampling (SRS).
  • To propose non-parametric and maximum likelihood estimators for population parameters using RSS data with tie information.

Main Methods:

  • Comparison of non-representative extreme samples under RSS and SRS.
  • Development of non-parametric and maximum likelihood estimators for population parameters.
  • Extensive numerical simulations to evaluate estimator performance under various factors (ranking ability, ties, categories, population setting).

Main Results:

  • Ranked set sampling (RSS) can mitigate issues with non-representative extreme samples compared to SRS.
  • The proposed estimators demonstrate reliable performance in extensive numerical studies.
  • The effectiveness of estimators is influenced by ranking ability, tie mechanisms, and population characteristics.

Conclusions:

  • Ranked set sampling (RSS) provides a valuable framework for analyzing ordinal data, especially in resource-constrained scenarios.
  • The developed estimators offer improved methods for parameter estimation in ordinal populations.
  • The study successfully applied these methods to bone disorder data, estimating proportions of osteopenia and osteoporosis.