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An overview of the variables selection methods for the minimum sum of absolute errors regression
Carmen D S André1, Subhash C Narula, Silvia N Elian
1Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CP-66281, CEP 05315-970, São Paulo, Brazil. tuca@ime.usp.br
Statistics in Medicine
|June 24, 2003
Summary
Minimum sum of absolute errors regression offers a robust alternative to least squares regression, especially with outliers or long-tailed distributions. This study reviews methods for variable selection in minimum sum of absolute errors models.
Area of Science:
- Statistics
- Regression Analysis
Background:
- Least squares regression is sensitive to outliers and assumes normally distributed errors.
- Minimum sum of absolute errors (MSAE) regression provides robustness when these assumptions are violated.
- Variable selection is crucial for parsimonious and interpretable models, but less documented for MSAE than for least squares.
Purpose of the Study:
- To provide an overview of variable selection procedures for MSAE regression.
- To present criteria for selecting parsimonious MSAE models.
Main Methods:
- Review of existing literature on variable selection techniques applicable to MSAE regression.
- Discussion of model selection criteria tailored for MSAE.
Main Results:
- MSAE regression is advantageous with non-normal error distributions, long tails, and outliers.
- Variable selection methods for MSAE, while less established than for least squares, are essential for model simplification.
- Criteria for model selection in MSAE are presented.
Conclusions:
- MSAE regression is a valuable tool for robust statistical modeling.
- Effective variable selection enhances the utility and interpretability of MSAE models.