Improved regression in ratio type estimators based on robust M-estimation.

Area of Science:

• Statistics
• Survey Methodology

Background:

• Estimating finite population means is crucial in statistical analysis.
• Outliers in datasets can significantly skew traditional estimation methods.
• Robust statistical techniques are needed to handle data with extreme values.

Purpose of the Study:

• To propose a novel robust ratio-type estimator for finite population mean estimation.
• To address the challenge of outliers in simple random sampling (SRS).
• To enhance the efficiency and reliability of mean estimation in the presence of unusual data points.

Main Methods:

• Development of a new robust ratio-type estimator utilizing the Uk's redescending M-estimator.
• Derivation of the Mean Square Error (MSE) equation using first-order approximation.
• Comparative analysis against traditional ratio-type estimators, robust regression estimators, and existing redescending M-estimators.

Main Results:

• The proposed estimator's MSE was theoretically derived and analyzed.
• Empirical validation through a real-life dataset and simulation studies.
• Demonstrated superior efficiency of the proposed estimator over existing methods.

Conclusions:

• The novel robust ratio-type estimator provides a more efficient and reliable method for estimating finite population means.
• The proposed estimator effectively mitigates the impact of outliers in SRS data.
• This research contributes a valuable tool for robust statistical inference in survey sampling.