Estimation of population variance under ranked set sampling method by using the ratio of supplementary information...

Area of Science:

• Statistics
• Biostatistics
• Medical Research

Background:

• Costly sample collection and measurement in biological/medical research often compromise inferential accuracy.
• Ranked set sampling (RSS) offers a more efficient alternative for data collection in such scenarios.
• Auxiliary information can further enhance the performance of statistical estimators.

Purpose of the Study:

• To propose two generalized classes of estimators for population variance using RSS and auxiliary information.
• To analyze the bias and mean square errors of the proposed estimators.
• To evaluate the performance of the proposed estimators through simulation and real-data application.

Main Methods:

• Development of two generalized classes of estimators utilizing ranked set sampling (RSS) and auxiliary variable information.
• Derivation of bias and mean square errors up to the first order of approximation.
• Conducting simulation studies with varying sample sizes and a real-life data application on fetal gestational age variance.

Main Results:

• The proposed generalized classes of estimators demonstrate improved accuracy in estimating population variance.
• Ranked set sampling (RSS) design proved to be more accurate than simple random sampling for hard-to-measure or destructive sampling units.
• The real-life data application confirmed the effectiveness of RSS in estimating the variance of fetal gestational age.

Conclusions:

• Ranked set sampling (RSS) combined with auxiliary information provides a robust and accurate method for population variance estimation in resource-intensive research settings.
• The proposed estimators offer a valuable tool for researchers dealing with destructive or costly data collection.
• RSS is recommended over simple random sampling for precise variance estimation in challenging biological and medical research contexts.