A Mathematical Programming Approach for Improving the Robustness of Lad Regression

22 Pages Posted: 3 Nov 2008

See all articles by Avi Giloni

Avi Giloni

Independent

Bhaskar Sengupta

affiliation not provided to SSRN

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business; New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: July 2004

Abstract

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used fora 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 demonstratethat our problem is equivalent to one similar to the knapsack problem and then solveit for a special case. We then generalize this solution to general regression designs.Furthermore, we provide an efficient algorithm to solve the general non-linear, mixed integer programming problem when the number of predictors is small. We show theefficacy of the weighted LAD estimator using numerical examples.

Keywords: Algorithms, Breakdown point, Knapsack problem, Nonlinear mixed integer programming, Robust regression

Suggested Citation

Giloni, Avi and Sengupta, Bhaskar and Simonoff, Jeffrey S., A Mathematical Programming Approach for Improving the Robustness of Lad Regression (July 2004). Statistics Working Papers Series, Vol. , pp. -, 2004. Available at SSRN: https://ssrn.com/abstract=1293593

Avi Giloni (Contact Author)

Independent

No Address Available

Bhaskar Sengupta

affiliation not provided to SSRN

No Address Available

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

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