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.

中文翻译：

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具有结构化协方差矩阵的线性模型的高分解点高效估计器

我们为平衡线性模型中回归参数的估计方法提供了一种统一的方法，该方法具有结构化的协方差矩阵，该矩阵结合了高分解点和有界影响以及具有多元正态误差的模型的高渐近效率。主要感兴趣的是线性混合效应模型，但我们的方法还包括其他几个标准的多元模型，例如多元回归、多元回归和多元位置和散布。我们为估计量和对应泛函的存在提供了充分条件，建立了一致性和渐近正态性等渐近性质，并推导出了它们在击穿点和影响函数方面的鲁棒性。所有结果都是针对一般可识别的协方差结构获得的，并且是在观察分布的温和条件下建立的，这远远超出了具有椭圆轮廓密度的模型。我们的一些结果是新的，而另一些则比文献中的现有结果更普遍。通过这种方式，本手稿在各种多元模型中以高效率完成并改进了高分解估计的结果。