关于位置泛函和散布泛函的一些事实
Some facts about functionals of location and scatter
摘要：
假设一个似然函数，包括一个局部Glivenko-Cantelli条件，意味着存在的M-估计收敛到一个M-功能。分散矩阵值估计，定义在${\Bbb{R}}^d$上的所有经验措施，为$d\geq 2$，并在所有，包括奇异，仿射变换下的等变，被证明是常数倍的样本协方差阵。所以，如果是弱连续的，它们必须同为0。结果的存在性和可微性的位置和散射泛函，定义在一个弱密集，弱开集法律，通过椭圆对称t分布${\Bbb{R}}^d$，后续工作的肯特，泰勒和Dümbgen。
英文摘要：
Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for $d\geq 2$, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they must be identically 0. Results are stated on existence and differentiability of location and scatter functionals, defined on a weakly dense, weakly open set of laws, via elliptically symmetric t distributions on ${\Bbb{R}}^d$, following up on work of Kent, Tyler, and Dümbgen.
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