A note on the uniform asymptotic normality of location M-estimates
A note on the uniform asymptotic normality of location M-estimates
复制标题
关于位置 M 估计的均匀渐近正态性的注解
DOI：
10.1007/s00184-005-0006-y
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
R. Zamar
中科院分区：
文献类型：
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作者：
J. Berrendero;R. Zamar
在鲁棒性框架中，数据背后的参数模型通常嵌入在其他合理分布的邻域中。因此，稳健估计的渐近性质在整个可能的模型集上应该是一致的。在本文中，我们研究了位置M-估计计算与以前的广义S-尺度，并表明，在一定的正则性条件下，他们是一致渐近正常的污染的邻域大小已知。在邻域的大小和GS尺度的崩溃点之间存在权衡，但是可以调整估计值，使得它们具有50%的崩溃点，而在包含高达25%的污染的邻域上确保一致渐近正态性。或者，可以将分解点和邻域的大小都选择为38%。这些结果比Salibian-Barrera和Zelvis（2004）最近获得的结果有所改进。
In the robustness framework, the parametric model underlying the data is usually embedded in a neighborhood of other plausible distributions. Accordingly, the asymptotic properties of robust estimates should be uniform over the whole set of possible models. In this paper, we study location M-estimates calculated with a previous generalized S-scale and show that, under some regularity conditions, they are uniformly asymptotically normal over contamination neighborhoods of known size. There is a trade off between the size of the neighborhood and the breakdown point of the GS-scale, but it is possible to adjust the estimates so that they have 50% breakdown point whereas the uniform asymptotic normality is ensured over neighborhoods that contain up to 25% of contamination. Alternatively, both the breakdown point and the size of the neighborhood could be chosen to be 38%. These results represent an improvement over those obtained recently by Salibian-Barrera and Zamar (2004)
DOI：
10.1016/b978-0-12-386908-1.00037-9
发表时间：
2018-11
期刊：
Wiley Series in Probability and Statistics
影响因子：
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作者：
Bruce E. Blaine
通讯作者：
Bruce E. Blaine