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.

翻译：我们为多种变式线性模型提出了一组稳健的估计数。根据MM估算方法(Yohai 1987年),我们同时估算了误差的回归系数和共变量矩阵。这些估计数在高斯误差下具有高分点和高吸附效率。我们证明,假设使用椭圆分布的误差,这种误差具有一致性和无症状的正常性。我们描述了计算这些估计数的迭代算法。通过模拟数据和真实数据来证明拟议估计数对其竞争者的优势。