Estimation of population median using bivariate auxiliary information in simple random sampling

Area of Science:

• Statistics
• Statistical Inference
• Robust Statistics

Background:

• Accurate estimation of population median is crucial in statistical analysis.
• Existing estimators often fail in the presence of outliers or extreme observations.
• Robust statistical methods are needed to address data contamination.

Purpose of the Study:

• To develop an enhanced class of robust estimators for population median.
• To improve estimation efficiency in simple random sampling with outliers.
• To address the limitations of traditional estimators when extreme values are present.

Main Methods:

• Proposed estimators are a mixture of bivariate auxiliary information and robust measures.
• Utilized a linear combination of deciles mean, tri-mean, and Hodges-Lehmann estimator.
• Evaluated mathematical properties including bias and mean squared error.
• Assessed performance using real-life datasets with outliers and a simulation study.

Main Results:

• The newly suggested robust estimators demonstrate superior performance compared to existing methods.
• Theoretical and numerical findings confirm the enhanced efficiency of the proposed estimators.
• The estimators effectively handle outliers, providing more reliable population median estimates.

Conclusions:

• The developed robust estimators offer a significant improvement for population median estimation, especially in datasets with extreme values.
• The proposed methods provide a valuable alternative for robust statistical inference under simple random sampling.
• The study highlights the importance of robust techniques in practical data analysis scenarios.