A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators

Abstrakt

While various robust regression estimators are available for the standard linear regression model, there have not been sufficient comparisons of the performance of individual robust estimators over real or simulated datasets. In general, a reliable robust estimator of regression parameters should be not only consistent but at the same time should have a relatively small variability, i.e. the variances of individual regression parameters should be small. The aim of this paper is to compare the variability of S­estimators, MM­estimators, least trimmed squares, and least weighted squares estimators. While they all are consistent under general assumptions, the asymptotic covariance matrix of the least weighted squares remains infeasible, because the only available formula for its computation depends on the unknown random errors. Thus, we take resort to a nonparametric bootstrap comparison of variability of different robust regression estimators. It turns out that the best results are obtained either with MM­estimators, or with the least weighted squares with suitable weights; the latter estimator is especially recommendable for small sample sizes.