标题： 结构协方差矩阵估计量的渐近性质 显示英文标题

标题： Asymptotics of estimators for structured covariance matrices

摘要： 我们证明了一个具有结构化协方差矩阵的估计量序列的极限方差具有一般形式，该形式表现为某种随机矩阵（径向型）的缩放投影的方差，同时对于相应的方差分量向量的估计量序列也得到了类似的结果。 这些结果通过各种多元统计模型中线性协方差结构的估计量的极限行为进行了说明。 我们还推导出相应泛函的影响函数的特征刻画。 此外，我们推导出此类估计量及其相应泛函的尺度不变映射的极限分布和影响函数。 由此可得，可以通过单一标量比较结构化协方差矩阵形状分量的不同估计量的渐近相对效率，并且可以通过单一指标比较相应影响函数的粗误差敏感性。 对于归一化方差分量估计量，也得到了类似的结果。 我们将我们的结果应用于研究S-估计量的效率、粗误差敏感性和破裂点如何随着归一化方差分量的截断值的变化而同时受到影响。 显示英文摘要

摘要： We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is obtained for the corresponding sequence of estimators for the vector of variance components. These results are illustrated by the limiting behavior of estimators for a linear covariance structure in a variety of multivariate statistical models. We also derive a characterization for the influence function of corresponding functionals. Furthermore, we derive the limiting distribution and influence function of scale invariant mappings of such estimators and their corresponding functionals. As a consequence, the asymptotic relative efficiency of different estimators for the shape component of a structured covariance matrix can be compared by means of a single scalar and the gross error sensitivity of the corresponding influence functions can be compared by means of a single index. Similar results are obtained for estimators of the normalized vector of variance components. We apply our results to investigate how the efficiency, gross error sensitivity, and breakdown point of S-estimators for the normalized variance components are affected simultaneously by varying their cutoff value.