Least Median of Squares Regression
提出一种新的稳健回归方法，用残差平方的中位数替代传统的最小二乘和，能抵抗近50%的数据污染，在简单回归中对应覆盖半数观测的最窄条带。
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.