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Advances in Operations Research
Volume 2011, Article ID 263762, 18 pages
Research Article

Outlier-Resistant 𝐿 𝟏 Orthogonal Regression via the Reformulation-Linearization Technique

Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, P.O. Box 843083, 1015 Floyd Avenue, Richmond, VA 23284, USA

Received 9 September 2010; Revised 7 January 2011; Accepted 14 January 2011

Academic Editor: I. L. Averbakh

Copyright © 2011 J. Paul Brooks and Edward L. Boone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. 𝐿 2 -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 𝐿 1 -norm orthogonal regression method ( 𝐿 1 OR) 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.