A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitiv...

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Bibliographic Details
Published in:Naval research logistics Vol. 53; no. 4; pp. 261 - 271
Main Authors: Giloni, Avi, Sengupta, Bhaskar, Simonoff, Jeffrey S.
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.06.2006
Subjects:
algorithms
breakdown point
knapsack problem
nonlinear mixed integer programming
robust regression
ISSN:0894-069X, 1520-6750
Online Access:Get full text
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Summary:This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006
Bibliography:ArticleID:NAV20139
istex:313912C001F2BEE9ECEFF10878B08560B8C0A9DE
ark:/67375/WNG-SK6HSSM7-F
This work was done when the author was at Yeshiva University.
ISSN:0894-069X
1520-6750
DOI:10.1002/nav.20139