Constrained M-estimation for multivariate location and scatter
Constrained M-estimation for multivariate location and scatter
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DOI：
10.1214/aos/1032526973
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发表时间：
1996-06
影响因子：
4.5
通讯作者：
J. Kent;David E. Tyler
中科院分区：
文献类型：
--
作者：
J. Kent;David E. Tyler
考虑从一组多元数据中估计位置向量和散布矩阵的问题。稳健估计的两个标准类别是M-估计和S-估计。可以调整M-估计以给出良好的局部鲁棒性，例如良好的效率和在底层分布（例如多元正态分布）上的影响函数的良好界限。然而，M-估计遭受在高维度的不良击穿特性。另一方面，S-估计可以被调整为具有良好的分解特性，但是当以这种方式调整时，它们往往会遭受较差的局部鲁棒性。本文提出了一种混合估计，称为约束M-估计，它结合了良好的局部和良好的全局鲁棒性。
Consider the problem of estimating the location vector and scatter matrix from a set of multivariate data. Two standard classes of robust estimates are M-estimates and S-estimates. The M-estimates can be tuned to give good local robustness properties, such as good efficiency and a good bound on the influence function at an underlying distribution such as the multivariate normal. However, M-estimates suffer from poor breakdown properties in high dimensions. On the other hand, S-estimates can be tuned to have good breakdown properties, but when tuned in this way, they tend to suffer from poor local robustness properties. In this paper a hybrid estimate called a constrained M-estimate is proposed which combines both good local and good global robustness properties.