The minimum sum of absolute errors regression: a robust alternative to the least squares regression

Area of Science:

• Statistics
• Biostatistics
• Regression Analysis

Background:

• Least squares regression is widely used but sensitive to outliers and non-normal error distributions.
• Robust regression methods are needed for data with deviations from standard assumptions.
• Minimum sum of absolute errors (MSAE) regression is a viable robust alternative.

Purpose of the Study:

• To introduce and illustrate the application of minimum sum of absolute errors regression.
• To demonstrate the advantages of MSAE regression over least squares regression in specific scenarios.
• To highlight the interpretation of findings from MSAE analysis using real-world data.

Main Methods:

• Application of minimum sum of absolute errors regression technique.
• Comparative analysis contrasting MSAE with least squares regression.
• Illustration using data from an interstitial lung disease study.

Main Results:

• MSAE regression demonstrates greater robustness in the presence of outliers or long-tailed error distributions.
• Analysis reveals potential issues with least squares regression in such scenarios.
• MSAE analysis provides a more reliable interpretation of the interstitial lung disease data.

Conclusions:

• Minimum sum of absolute errors regression is a valuable tool for robust statistical analysis.
• It effectively addresses limitations of least squares regression when data deviates from assumptions.
• The study underscores the importance of choosing appropriate regression methods for accurate data interpretation.