Bootstrapping robust estimates of regression
Bootstrapping robust estimates of regression
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DOI：
10.1214/aos/1021379865
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发表时间：
2002-04-01
影响因子：
4.5
通讯作者：
Zamar, RH
中科院分区：
文献类型：
--
作者：
Salibian-Barrera, M;Zamar, RH
我们引入了一种新的计算机密集型方法来估计稳健回归估计的分布。我们方法背后的基本思想是引导估计的重新加权表示。为了得到一个渐近正确的Bootstrap方法，我们将辅助尺度估计包括在估计的重新加权表示中。我们的方法在计算上很简单，因为对于每个Bootstrap样本，我们只需要求解一个线性方程组。我们使用的权重是残差绝对值的递减函数，因此外部观测得到的权重较小。这导致了一种自举方法，该方法可以抵抗数据中异常值的存在。用这种方法得到的分位数估计的崩溃点比用Bootstrap得到的要高。我们在两个数据集上说明了我们的方法，并报告了关于线性模型参数的可信区间的蒙特卡罗实验的结果。
We introduce a new computer-intensive method to estimate the distribution of robust regression estimates. The basic idea behind Our method is to bootstrap a reweighted representation of the estimates. To obtain a bootstrap method that is asymptotically correct, we include the auxiliary scale estimate in our reweighted representation of the estimates. Our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations. The weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights. This results in a bootstrap method that is resistant to the presence of outliers in the data. The breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap. We illustrate our method on two datasets and we report the results of a Monte Carlo experiment on confidence intervals for the parameters of the linear model.