Enhancing mean estimators in median ranked set sampling with dual auxiliary information

Area of Science:

• Statistics
• Survey Methodology
• Statistical Inference

Background:

• Median Ranked Set Sampling (MRSS) is efficient when direct measurement is difficult.
• Existing methods often use one auxiliary variable for population mean estimation.
• There's a need for more precise estimators in complex scenarios.

Purpose of the Study:

• To develop a novel regression-type estimator using two auxiliary variables within the MRSS framework.
• To theoretically derive the minimum mean square error (MSE) for the proposed estimator.
• To assess the practical performance of the new estimator.

Main Methods:

• Extension of existing MRSS estimation techniques.
• Development of a new regression-type estimator incorporating two auxiliary variables.
• Theoretical derivation of the Minimum Mean Square Error (MSE).
• Validation through simulation studies and real-world data analysis.

Main Results:

• The proposed regression-type estimator demonstrates improved precision compared to existing methods.
• Theoretical MSE calculations support the estimator's efficiency.
• Empirical results from simulations and real data confirm the estimator's practical applicability and superiority.

Conclusions:

• The novel MRSS-based regression estimator with two auxiliary variables offers a more precise approach to population mean estimation.
• This method is particularly valuable when direct measurement is challenging or costly.
• The findings contribute to advancing statistical sampling techniques for improved data analysis.