Outlier-Resistant 𝐿𝟏 Orthogonal Regression via the Reformulation-Linearization Technique

Autor: J. Paul Brooks, Edward L. Boone
Jazyk: angličtina
Rok vydání: 2011
Předmět:
Zdroj: Advances in Operations Research, Vol 2011 (2011)
Druh dokumentu: article
ISSN: 1687-9147
1687-9155
DOI: 10.1155/2011/263762
Popis: Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. 𝐿2-based methods such as ordinary least squares and orthogonal regression can be used to determine this relationship. However, both of these methods become impaired when influential values are present. This problem becomes compounded when outliers confound standard diagnostics. This work proposes an 𝐿1-norm orthogonal regression method (𝐿1OR) formulated as a nonconvex optimization problem. Solution strategies for finding globally optimal solutions are presented. Simulation studies are conducted to assess the resistance of the method to outliers and the consistency of the method. The method is also applied to real-world data arising from an environmental science application.
Databáze: Directory of Open Access Journals
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