Alternatives to the Median Absolute Deviation
Alternatives to the Median Absolute Deviation
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DOI：
10.1080/01621459.1993.10476408
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发表时间：
1993
影响因子：
3.7
通讯作者：
P. Rousseeuw;C. Croux
中科院分区：
文献类型：
--
作者：
P. Rousseeuw;C. Croux
摘要 在鲁棒估计中，人们经常需要对规模进行初始或辅助估计。对于这一点，通常取中值绝对偏差 MAD n = 1.4826 med, {|xi − med j x j |}，因为它有一个简单的显式公式，需要很少的计算时间，并且正如其有界影响函数和 50% 故障点所证明的那样，非常鲁棒。但在两个方面仍有改进的空间：MAD n 针对对称分布及其低（37％）的高斯效率。在本文中，我们着手构建更高效的显式 50% 细分规模估算器。我们考虑估计量 Sn = 1.1926 med, {med j | xi − xj |} 和由距离 {|xi − x j | 的 0.25 分位数给出的估计量 Qn；我 < j}。请注意，Sn 和 Qn 不需要任何位置估计。 Sn 和 Qn 都可以使用 O(n log n) 时间和 O(n) 存储来计算。 Sn的高斯效率为58%，而Qn达到82%。我们通过它们的影响函数、它们的b...来研究Sn和Qn。
Abstract In robust estimation one frequently needs an initial or auxiliary estimate of scale. For this one usually takes the median absolute deviation MAD n = 1.4826 med, {|xi − med j x j |}, because it has a simple explicit formula, needs little computation time, and is very robust as witnessed by its bounded influence function and its 50% breakdown point. But there is still room for improvement in two areas: the fact that MAD n is aimed at symmetric distributions and its low (37%) Gaussian efficiency. In this article we set out to construct explicit and 50% breakdown scale estimators that are more efficient. We consider the estimator Sn = 1.1926 med, {med j | xi − xj |} and the estimator Qn given by the .25 quantile of the distances {|xi − x j |; i < j}. Note that Sn and Qn do not need any location estimate. Both Sn and Qn can be computed using O(n log n) time and O(n) storage. The Gaussian efficiency of Sn is 58%, whereas Qn attains 82%. We study Sn and Qn by means of their influence functions, their b...