A working likelihood approach for robust regression.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Robust statistical methods are crucial for reliable parameter estimation in the presence of outliers.
• The selection of regularization parameters significantly influences the efficiency of parameter estimators.
• Existing methods often require a fixed regularization parameter, limiting adaptability to data contamination levels.

Purpose of the Study:

• To develop a robust approach for parameter estimation that optimizes regularization parameter selection.
• To enhance the efficiency of regression parameter estimation by simultaneously estimating the tuning parameter.
• To provide a method that adapts the regularization parameter based on the extent of data contamination.

Main Methods:

• Constructed a novel likelihood function for simultaneous estimation of regression and tuning parameters.
• Employed a "working" likelihood function, not assuming it generates the data, for efficient regression parameter estimation.
• Conducted extensive simulation studies across various data scenarios to evaluate the method's performance.

Main Results:

• The proposed method effectively determines the regularization parameter based on data contamination.
• Demonstrated significant efficiency gains: up to 40% for heavy-tailed distributions and 468% for heteroscedastic variance cases compared to Huber's method.
• Analyzed real-world datasets from diabetic and mortality studies for practical illustration.

Conclusions:

• The developed method offers a superior, adaptive approach to robust parameter estimation.
• Achieves substantial efficiency improvements over traditional methods, particularly in challenging data conditions.
• Validated through simulations and real-world data analysis, showing practical applicability.