Uniqueness of the least‐distances estimator in regression models with multivariate response

TLDR: In this article, the authors show that in a regression model with multivariate response, the least-distances method typically yields quantities that exhibit uniqueness properties that are similar to those obtained by the least squares method.

Abstract: In a regression model with univariate response, the quantities derived from the least-absolute-deviations method need not be unique. In this note, we show that, contrary to the univariate case, in a regression model with multivariate response, the least-distances method typically yields quantities that exhibit uniqueness properties that are similar to those obtained by the least-squares method. Dans un contexte de regression avec une reponse univariee, les quantitees obtenues par la methode des moindres deviations absolues ne sont pas, en general, uniques. Dans cette note, on montre que, contrairement au cas univarie, les quantites obtenues par la methode des moindres distances dans le cas d'une reponse multivariee presentent des proprietes d'unicite similaires a celles obtenues par la methode des moindres carres.