Asymptotic Theory of Least Absolute Error Regression

Abstract In the general linear model with independent and identically distributed errors and distribution function F, the estimator which minimizes the sum of absolute residuals is demonstrated to be consistent and asymptotically Gaussian with covariance matrix ω2 Q -1, where Q = lim T -1 X'X and ω2 is the asymptotic variance of the ordinary sample median from samples with distribution F. Thus the least absolute error estimator has strictly smaller asymptotic confidence ellipsoids than the least squares estimator for linear models from any F for which the sample median is a more efficient estimator of location than the sample mean.