Transformation-based median estimation under skewed-symmetric distributions with long-memory data applications

Area of Science:

• Statistics
• Survey Methodology

Background:

• Median estimation in finite populations is crucial for data analysis.
• Traditional methods can be costly and less accurate with limited auxiliary information.
• Double-sampling frameworks offer a way to improve efficiency by using supplementary data.

Purpose of the Study:

• To develop enhanced median estimators for finite populations using a double-sampling framework.
• To utilize transformation-based methods for efficient use of limited auxiliary information.
• To assess the accuracy and robustness of the proposed estimators.

Main Methods:

• Formulation of enhanced median estimators within a double-sampling design.
• Application of transformation-based methods to leverage auxiliary information.
• Derivation of first-order approximations for bias and mean squared error.
• Monte Carlo simulations using real-life datasets and skewed distributions.
• Investigation of robustness using fractional Gaussian noise (fGn) and ARFIMA models.

Main Results:

• The proposed estimators demonstrate superior accuracy and efficiency compared to existing methods, as measured by percent relative efficiency (PRE).
• Performance shows only a minor decrease in efficiency even with increased long-range dependence in auxiliary variables.
• Graphical analyses confirm the reliability and stability of the estimators.

Conclusions:

• The new transformation-based median estimators provide stable and economical techniques for median estimation in two-phase sampling.
• These estimators are effective even when auxiliary information exhibits long-memory or fractal behavior.
• The methods offer a practical approach to enhance statistical estimation accuracy while managing data collection costs.