Median Estimation with Quantile Transformations: Applications to Stratified Two-Phase Sampling

Area of Science:

• Statistics
• Survey Methodology

Background:

• Traditional median estimators often assume normality and are sensitive to outliers.
• This sensitivity limits their reliability in real-world applications with non-normal or skewed data.

Purpose of the Study:

• To introduce novel quintile-based median estimators.
• To enhance accuracy and robustness in stratified two-phase sampling.
• To improve the efficiency of median estimation using auxiliary data.

Main Methods:

• Utilized transformation methods within a stratified two-phase sampling framework.
• Developed quintile-based median estimators.
• Derived bias and mean squared error (MSE) expressions via first-order approximations.
• Evaluated estimator efficiency using MSE.

Main Results:

• Proposed estimators demonstrated superior performance in simulations under skewed distributions.
• Analysis on real population datasets confirmed the effectiveness of the new methods.
• The quintile-based estimators achieved higher precision and effectiveness compared to existing approaches.

Conclusions:

• The novel quintile-based median estimators are robust and accurate for practical applications.
• These estimators provide a more effective alternative for median estimation, particularly in stratified sampling scenarios.
• The methods enhance the utility of auxiliary data and perform well with heterogeneous strata.