M estimation of multivariate regressions

Roger Koenker, Stephen Portnoy

Research output: Contribution to journalArticle


Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model. These weighted M estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator. Comparisons for the l1, least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions. An example reanalyzing the Grunfeld investment data using a smooth “l1-like” M estimator is discussed in detail. In contrast to recent work of Hampel, Ronchetti, Rousseeuw, and Stahel (1986), Rousseeuw (1987), and Oja (1983), the methods studied here are not affine equivariant; some remarks on the potential significance of this failing conclude the article.

Original languageEnglish (US)
Pages (from-to)1060-1068
Number of pages9
JournalJournal of the American Statistical Association
Issue number412
StatePublished - Dec 1990


  • L estimation
  • Robustness
  • Seemingly unrelated regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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