Document Type
Article
Original Publication Date
2011
Journal/Book/Conference Title
Advances in Operations Research
Volume
2011
Issue
Article ID 263762, 18 pages
DOI
10.1155/2011/263762
Date of Submission
July 2014
Abstract
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.
Rights
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.
Is Part Of
VCU Statistical Sciences and Operations Research Faculty Publications
Comments
Originally published open access online through Hindawi at http://dx.doi.org/10.1155/2011/263762