英文文献：Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood-最小平方修剪和最小平方估计的中位数是最大似然的模型
英文文献作者：Vanessa Berenguer-Rico,S?ren Johansen,Bent Nielsen
英文文献摘要：
The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h good observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be sqrt(h) consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.

最小二乘(LTS)和最小二乘(LMS)估计量是常用的稳健回归估计量。估计值背后的思想是，对于给定的h，在n个观测中找到h个良好观测的子样本并估计该子样本上的回归。我们发现分别基于正态分布或均匀分布的模型中，这些估计量是极大似然的。在这些模型中，我们提供了位置-尺度情况下的渐近理论。发现LTS估计量为sqrt(h)一致且渐近标准正态。LMS估计量是h一致的，且渐近拉普拉斯。