We provide a unified approach to a method of estimation of the regression parameter in balanced linear models with a structured covariance matrix that combines a high breakdown point and bounded influence with high asymptotic efficiency at models with multivariate normal errors. Of main interest are linear mixed effects models, but our approach also includes several other standard multivariate models, such as multiple regression, multivariate regression, and multivariate location and scatter. We provide sufficient conditions for the existence of the estimators and corresponding functionals, establish asymptotic properties such as consistency and asymptotic normality, and derive their robustness properties in terms of breakdown point and influence function. All the results are obtained for general identifiable covariance structures and are established under mild conditions on the distribution of the observations, which goes far beyond models with elliptically contoured densities. Some of our results are new and others are more general than existing ones in the literature. In this way this manuscript completes and improves results on high breakdown estimation with high efficiency in a wide variety of multivariate models.

翻译：本文提出一种统一方法，针对具有结构化协方差矩阵的平衡线性模型中的回归参数估计，该方法在高崩溃点与有界影响性的基础上，在多元正态误差模型下实现了高渐近效率。主要关注线性混合效应模型，但本文方法也涵盖其他标准多元模型，如多元回归、多变量回归以及多元位置与散度估计。我们给出了估计量及其泛函存在的充分条件，建立了相合性与渐近正态性等渐近性质，并基于崩溃点与影响函数推导了其稳健性特征。所有结果均针对一般可识别协方差结构获得，并在观测分布的温和条件下建立，其适用范围远超椭圆对称密度模型。本文部分结论为首次提出，另一些则较现有文献更为普适。由此，本手稿完善并改进了多种多元模型中兼具高崩溃点与高效率的估计理论。