A Bootstrap Comparison of Robust Regression Estimators

0564518 - ÚI 2023 RIV CZ eng C - Conference Paper (international conference)
Kalina, Jan - Janáček, Patrik
A Bootstrap Comparison of Robust Regression Estimators.
Mathematical Methods in Economics 2022: Proceedings. Jihlava: College of Polytechnics Jihlava, 2022 - (Vojáčková, H.), s. 161-167. ISBN 978-80-88064-62-6.
[MME 2022: International Conference on Mathematical Methods in Economics /40./. Jihlava (CZ), 07.09.2022-09.09.2022]
R&D Projects: GA ČR GA21-05325S
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : linear regression * robust estimation * nonparametric bootstrap * bootstrap hypothesis testing
OECD category: Statistics and probability; Statistics and probability (UTIA-B)
https://mme2022.vspj.cz/download/proceedings-4.pdf

The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
Permanent Link: https://hdl.handle.net/11104/0336179