Estimates of MM type for the multivariate linear model

TL;DR

This paper introduces a robust estimation method for multivariate linear models that combines high breakdown point and efficiency, with proven statistical properties and demonstrated advantages over existing methods.

Contribution

It develops a new class of MM-based estimators for multivariate linear models, estimating regression and covariance simultaneously with proven robustness and efficiency.

Findings

Estimates are robust with high breakdown point.

Estimates are asymptotically normal under elliptical errors.

Demonstrated advantages through simulations and real data.

Abstract

We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have both high breakdown point and high asymptotic efficiency under Gaussian errors. We prove consistency and asymptotic normality assuming errors with an elliptical distribution. We describe an iterative algorithm for the numerical calculation of these estimates. The advantages of the proposed estimates over their competitors are demonstrated through both simulated and real data.