Covariance matrices of S robust regression estimators

Asymptotic properties of robust regression estimators are well known. However, it is not always clear what is the best strategy for confidence intervals and hypothesis testing when the sample size is not very large, since the distribution of residuals coming from robust estimates has unknown properties for small samples. In the present work we propose an analysis of various strategies for estimating the variance-covariance matrix of the S estimators at the variation of n and p, considering different ρ functions. An adaptive correction strategy is proposed. In addition to the simulation study, an example on a benchmark dataset is shown.