Methodology based on the L₁-norm, in statistical inference

Abstract

This paper reviews some recent contributions to statistical methodology based on the L₁-norm as a robust alternative to that based on the least squares, Tests are developed using the medians instead of the means and least absolute deviations instead of least squares. Analogues of Hotelling's T² and tests based on the roots of a determinantal equation are derived using medians. Asymptotic inference procedures on regression parameters in the univariate linear model are reviewed and some suggestions are made for the elimination of nuisance parameters which occur in the asymptotic distributions. The results are extended to the multivarite linear model. Recent work on the asymptotic theory of inference on the parametrrs of a generalized multivariate linear model based on the method of least distances is discussed. New tests are developed using least distances estimators.