Least Median of Squares Regression
Least Median of Squares Regression
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DOI：
10.1080/01621459.1984.10477105
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发表时间：
1984-12
影响因子：
3.7
通讯作者：
P. Rousseeuw
中科院分区：
文献类型：
--
作者：
P. Rousseeuw
摘要经典最小二乘回归是最小化残差平方和。许多作者通过用其他东西（如绝对值）代替平方来产生更鲁棒的估计量版本。在这篇文章中，介绍了一种不同的方法，其中的总和是由平方残差的中位数。由此产生的估计可以抵抗近50%的数据中的污染的影响。在简单回归的特殊情况下，它对应于找到覆盖一半观测值的最西带。可以推广到多元定位、正交回归和线性模型中的假设检验。
Abstract Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.