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

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.