Robust estimation and variable selection in heteroscedastic linear regression

ABSTRACT

The paper concerns robust estimation and variable selection in heteroscedastic linear regression models. After a brief review of existing methods for estimation in such models, a robust S-estimation approach is discussed. For all methods concise descriptions of algorithms are provided. Little is available upon robust variable selection methods for heteroscedastic linear models. The paper gives essential contributions in the area of simultaneous robust estimation and variable selection, relying on basics of the nonnegative garrote method which has been proven to have very good practical as well as theoretical properties in the homoscedastic linear model context. Several numerical examples, simulations and analysis of real data, demonstrate the performances and practical use of the discussed methods. Moreover, we provide expressions for the influence functions of the estimators of the mean and the error variance parameters. Influence functions are plotted in a simple setting providing insights in the sensitivity of the estimators for a single outlying observation.

KEYWORDS:

• Heteroscedasticity
• influence function
• nonnegative garrote
• S-estimation
• variable selection

Acknowledgments

The authors are grateful to the anonymous reviewers for their comments on an earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by Federaal Wetenschapsbeleid IAP Research Networks [Network P7/06] of the Belgian State (Belgian Science Policy), the Research Fund of the KU Leuven [project GOA/12/014], and the Research Foundation Flanders (FWO) [grant 1.5.137.13N].