论文标题
具有结构化协方差矩阵的线性模型的高效估计器具有高分解点
Highly Efficient Estimators with High Breakdown Point for Linear Models with Structured Covariance Matrices
论文作者
论文摘要
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，该方法在具有多变量正常误差的模型上结合了高分解点和有界影响与高渐近效率的结构化协方差矩阵。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种标准的多元模型，例如多元回归，多元回归以及多元位置和散布。我们为存在估计量和相应功能的存在提供了足够的条件，建立了渐近特性，例如一致性和渐近正态性，并根据分解点和影响函数得出其鲁棒性。所有结果均可用于通用可识别的协方差结构，并在温和条件下建立在观测值的分布下，这远远超出了具有椭圆形构成密度的模型。我们的一些结果是新的，其他结果比文献中的现有结果更一般。通过这种方式，该手稿完成并改善了高分估计的结果，并在各种多元模型中具有高效率。
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.
