标题： 具有分类预测变量的S估计量的非奇异子抽样 显示英文标题

标题： Nonsingular subsampling for S-estimators with categorical predictors

摘要： 许多线性回归S估计量算法的一个重要组成部分是随机子抽样。 对于只有连续预测变量的问题，简单随机子抽样是一种可靠的方法来生成初始的系数估计值，然后可以进一步细化这些估计值。 然而，对于具有分类预测变量的数据，随机子抽样通常不起作用，从而限制了这种原本很好的估计器的使用。 这也使得稳健线性回归的估计器选择依赖于预测变量的类型，在实践中这是一个不必要的麻烦。 对于具有分类预测变量的数据，随机子抽样常常会产生奇异子样本。 由于这些子样本不能用于计算系数估计值，必须将其丢弃。 这使得随机子抽样变得缓慢，特别是当某些分类预测变量的水平频率较低时，并使算法对于此类问题不可行。 本文介绍了一种改进的子抽样算法，该算法只会生成非奇异子样本。 我们称之为非奇异子抽样。 对于具有连续变量的数据，它与简单的随机子抽样一样快，但对于具有分类预测变量的数据则快得多。 这是通过使用一种修改后的LU分解算法实现的，该算法结合了样本生成和最小二乘问题求解的过程。 显示英文摘要

摘要： An integral part of many algorithms for S-estimators of linear regression is random subsampling. For problems with only continuous predictors simple random subsampling is a reliable method to generate initial coefficient estimates that can then be further refined. For data with categorical predictors, however, random subsampling often does not work, thus limiting the use of an otherwise fine estimator. This also makes the choice of estimator for robust linear regression dependent on the type of predictors, which is an unnecessary nuisance in practice. For data with categorical predictors random subsampling often generates singular subsamples. Since these subsamples cannot be used to calculate coefficient estimates, they have to be discarded. This makes random subsampling slow, especially if some levels of categorical predictors have low frequency, and renders the algorithms infeasible for such problems. This paper introduces an improved subsampling algorithm that only generates nonsingular subsamples. We call it nonsingular subsampling. For data with continuous variables it is as fast as simple random subsampling but much faster for data with categorical predictors. This is achieved by using a modified LU decomposition algorithm that combines the generation of a sample and the solving of the least squares problem.