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The minimum sum of absolute errors regression: a robust alternative to the least squares regression

✍ Scribed by Subhash C. Narula; Paulo H. N. Saldiva; Carmen D. S. Andre; Silvia N. Elian; Aurea Favero Ferreira; Vera Capelozzi

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
134 KB
Volume
18
Category
Article
ISSN
0277-6715

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✦ Synopsis

This paper concerns the minimum sum of absolute errors regression. It is a more robust alternative to the popular least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long tailed distribution, or the loss function is proportional to the absolute errors rather than their squared values. We use data from a study of interstitial lung disease to illustrate the method, interpret the "ndings, and contrast with least squares regression. We point out some of the problems with the least squares analysis and show how to avoid these with the minimum sum of absolute errors analysis.

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## 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