(DP 1983-04) Regression by Minimum Sum of Absolute Errors: Some Results

Abstract

In the multiple regression model y= xƒÒ + ƒÕ, the coefficient vector ƒÒ may be estimated by minimizing the sum of absolute errors (MSAE). This papers shows the following results under MSAE estimation: (1) If k coefficient ƒÒj are nonzeros, then the estimated regression equation accurately predicts at least k observations; (2) As in the case of least squares regression, ƒÒ has an infinite number of estimates in the presence of perfect multicollinearity.