Covariance matrices of S robust regression estimators. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Salini, S.; Laurini, F.; Morelli, G.; Riani, M.; Cerioli, A.
• Is Part Of: Journal of statistical computation and simulation. Volume 92:Issue 4(2022)
• Page Start: 724
• Page End: 747
• Publication Date: 2022-03-04
• Subjects: S-estimator -- Wald-type inference -- robust regression; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2021.1972300
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : 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.