S-estimation in linear models with structured covariance matrices
本文提出了一种统一方法，用于平衡线性模型中结构化协方差矩阵的S估计，涵盖线性混合效应模型、多元回归等，给出了存在性、渐近性质和稳健性结果，并通过模拟和儿童铅暴露治疗数据验证。
We provide a unified approach to S-estimation in balanced linear models with structured covariance matrices. Of main interest are S-estimators for linear mixed effects models, but our approach also includes S-estimators in several other standard multivariate models, such as multiple regression, multivariate regression and multivariate location and scatter. We provide sufficient conditions for the existence of S-functionals and S-estimators, 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 S-estimation in a wide variety of multivariate models. We illustrate our results by means of a simulation study and an application to data from a trial on the treatment of lead-exposed children.