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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/26318
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| Title: | A Mathematical Programming Approach for Improving the Robustness of LAD Regression |
| Authors: | Giloni, Avi
Sengupta, Bhaskar
Simonoff, Jeffrey |
| Keywords: | Algorithms
Breakdown point
Knapsack problem
Nonlinear mixed integer programming
Robust regression |
| Issue Date: | 23-Jul-2004 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-2004-2 |
| Abstract: | 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 one similar to 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 non-linear, mixed integer programming problem when the
number of predictors is small. We show the efficacy of the weighted LAD
estimator using numerical examples. |
| URI: | http://hdl.handle.net/2451/26318 |
| Appears in Collections: | IOMS: Statistics Working Papers
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