ALTERNATIVES TO THE MEDIAN ABSOLUTE DEVIATION
ALTERNATIVES TO THE MEDIAN ABSOLUTE DEVIATION
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DOI：
10.2307/2291267
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发表时间：
1993-12-01
影响因子：
3.7
通讯作者：
CROUX, C
中科院分区：
文献类型：
--
作者：
ROUSSEEUW, PJ;CROUX, C
在鲁棒估计中，经常需要对尺度进行初始或辅助估计。对于这一点，通常采用中位数绝对偏差MAD（n）= 1.4826 med（i）{\x（i）- med（j）x（j）\}，因为它具有简单的显式公式，需要很少的计算时间，并且通过其有界影响函数和其50%崩溃点证明是非常鲁棒的。但在两个方面仍有改进的空间：MAD（n）针对对称分布的事实和其低（37%）高斯效率。在这篇文章中，我们开始构建更有效的显式和50%分解尺度估计。我们考虑估计量S（n）= 1.1926 med（i）{med（j）\x（i）- x（j）}和由距离{\x（i）- x（j）\i < j}的.25分位数给出的估计量Q（n）。注意，S（n）和Q（n）不需要任何位置估计。（n）时间复杂度：O（n）时间复杂度：O（n）空间复杂度：O（n）空间复杂度：O（n）空间复杂度：O（n）空间复杂度：S（n）的高斯效率为58%，而Q（n）达到82%。我们研究S（n）和Q（n）的影响函数，他们的偏差曲线（内爆以及爆炸），和他们的有限样本性能。它们的行为也在非高斯模型中进行了比较，包括负指数模型，其中S（n）的粗差敏感性低于MAD。
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(i) {\x(i) - med(j)x(j)\}, because it has a simple explicit formula, needs little computation time, and is very robust a 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 S(n) = 1.1926 med(i) {med(j)\x(i) - x(j)} and the estimator Q(n) given by the.25 quantile of the distances {\x(i) - x(j)\i < j}. Note that S(n) and Q(n) do not need any location estimate. Both S(n) and Q(n) can be computed using O(n log n) time and O(n) storage. The Gaussian efficiency of S(n) is 58%, whereas Q(n) attains 82%. We study S(n) and Q(n) by means of their influence functions, their bias curves (for implosion as well as explosion), and their finite-sample performance. Their behavior is also compared at non-Gaussian models, including the negative exponential model where S(n) has a lower gross-error sensitivity than the MAD.