Comparison of Some Quick Algorithms for Robust Regression

摘要

Existing high-breakdown regression estimators need substantial computation time. In the paper, the authors propose two less time-consuming alternatives with a breakdown point of 1/3. This is not the highest value possible, but it is independent of the number of predictor variables. Both algorithms start by identifying unusual points by computationally cheap robust estimates of location and scale in x-space or (x,y)-space, and then apply L(1) regression to the remaining points. Two somewhat more refined variants of these methods are also discussed, both based on resampling, but using only a very limited number of subsamples. Some examples are given, and a small simulation study is presented. It appears that in these cases the new algorithms perform equally well as more time-consuming estimators. (Copyright (c) 1991 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)