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The minimum sum of absolute errors regression: a robust alternative to the least squares regression
Author(s) -
Narula Subhash C.,
Saldiva Paulo H. N.,
Andre Carmen D. S.,
Elian Silvia N.,
Ferreira Aurea Favero,
Capelozzi Vera
Publication year - 1999
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19990615)18:11<1401::aid-sim136>3.0.co;2-g
Subject(s) - robust regression , statistics , regression , least absolute deviations , total least squares , regression analysis , explained sum of squares , linear regression , mathematics , generalized least squares , regression diagnostic , econometrics , polynomial regression , estimator
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 findings, 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. Copyright © 1999 John Wiley & Sons, Ltd.