Robust Multivariate Regression

We introduce a robust method for multivariate regression, based on robust estimation of the joint location and scatter matrix of the explanatory and response variables. The resulting method has the appropriate equivariance properties, a bounded inuence function, and the same breakdown value as the initial estimators of location and scatter. To increase the efficiency we propose a reweighted estimator, which was selected from several possible reweighting schemes. Simulations show that the asymptotic properties of robustness and efficiency remain valid at finite samples. The method does not need much computation time, and is applied to chemical engineering data.