Asymptotic theory of least absolute error regression

Gilbert Bassett, Roger Koenker

Research output: Contribution to journalArticlepeer-review


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 ω2Q−1, where Q = lim T−1X′X and ω2is 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.

Original languageEnglish (US)
Pages (from-to)618-622
Number of pages5
JournalJournal of the American Statistical Association
Issue number363
StatePublished - Sep 1978


  • Asymptotic distribution theory
  • Least absolute error estimators
  • Linear models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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