Robust regression with asymmetric heavy-tail noise distributions

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Traditional robust regression methods assume symmetric noise, leading to biased estimators with asymmetric noise.
• Outliers significantly impact regression accuracy, especially under heavy-tailed noise distributions.

Purpose of the Study:

• To develop a new robust regression approach capable of handling asymmetric noise distributions.
• To improve regression accuracy in data-mining applications, particularly within the insurance industry.

Main Methods:

• Utilizing conditional quantile estimators to learn most model parameters, accepting their inherent bias for robustness.
• Employing a secondary parameter learning stage to correct and combine estimators, minimizing average squared error unbiasedly.
• Applying both linear and neural network predictors to artificial and real-world insurance datasets.

Main Results:

• The proposed method demonstrates clear advantages over traditional approaches.
• Experiments confirm the effectiveness of the new approach on both simulated and insurance data.
• The technique successfully handles asymmetric noise, yielding less biased regression estimators.

Conclusions:

• The novel robust regression method effectively addresses asymmetric noise distributions.
• This approach offers significant improvements for regression tasks in data-mining and insurance analytics.
• The combination of conditional quantile estimators and bias correction provides a powerful tool for robust modeling.