<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications, but can be also used as self-standing regression estimation procedures. Therefore, they need to be equipped by their own diagnostic tools. This paper is devoted to robust regression and presents three contributions to its diagnostic tools or estimating regression parameters under non-standard conditions. Firstly, we derive the Durbin-Watson test of independence of random regression errors for the regression median. The approach is based on the approximation to the exact null distribution of the test statistic. Secondly, we accompany the least trimmed squares estimator by a subjective criterion for selecting a suitable value of the trimming constant. Thirdly, we propose a robust version of the instrumental variables estimator. The new methods are illustrated on examples with real data and their advantages and limitations are discussed.</p></abstract>

Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications, but can be also used as self-standing regression estimation procedures. Therefore, they need to be equipped by their own diagnostic tools. This paper is devoted to robust regression and presents three contributions to its diagnostic tools or estimating regression parameters under non-standard conditions. Firstly, we derive the Durbin-Watson test of independence of random regression errors for the regression median. The approach is based on the approximation to the exact null distribution of the test statistic. Secondly, we accompany the least trimmed squares estimator by a subjective criterion for selecting a suitable value of the trimming constant. Thirdly, we propose a robust version of the instrumental variables estimator. The new methods are illustrated on examples with real data and their advantages and limitations are discussed.

Three contributions to robust regression diagnostics

Institute of Computer Science of the Czech Academy of Sciences Pod Vodárenskou věží 2, CZ-182 07 Praha 8, Czech Republic

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Three contributions to robust regression diagnostics"}

Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications,...

Three contributions to robust regression diagnostics

Published Online: Dec 30, 2015

Page range: 69 - 78

DOI: https://doi.org/10.1515/jamsi-2015-0013

© 2015 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.