A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.

0509646 - ÚI 2020 RIV CZ eng C - Conference Paper (international conference)
Kalina, Jan - Tobišková, Nicole - Tichavský, Jan
A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.
Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019. České Budějovice: University of South Bohemia in České Budějovice, Faculty of Economics, 2019 - (Houda, M.; Remeš, R.), s. 168-173. ISBN 978-80-7394-760-6.
[MME 2019: International Conference on Mathematical Methods in Economics /37./. České Budějovice (CZ), 11.09.2019-13.09.2019]
R&D Projects: GA ČR(CZ) GA19-05704S; GA ČR GA17-01251S
Institutional support: RVO:67985807
Keywords : robustness * linear regression * outliers * bootstrap * least weighted squares
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://mme2019.ef.jcu.cz/files/conference_proceedings.pdf

While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be still lacking. In general, a reliable robust estimator of regression parameters should be consistent and 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 S-estimators, MM-estimators, 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 MM-estimators, or with the least weighted squares with suitable weights. The latter estimator is especially recommendable for small sample sizes.
Permanent Link: http://hdl.handle.net/11104/0300321