Consistency and robustness properties of the S-nonnegative garrote estimator

ABSTRACT

This paper concerns a robust variable selection method in multiple linear regression: the robust S-nonnegative garrote variable selection method. In this paper the consistency of the method, both in terms of estimation and in terms of variable selection, is established. Moreover, the robustness properties of the method are further investigated by providing a lower bound for the breakdown point, and by deriving the influence function. The provided expressions nicely reveal the impact that the choice of an initial estimator has on the robustness properties of the variable selection method. Illustrative examples of influence functions for the S-nonnegative garrote as well as for the original (non-robust) nonnegative garrote variable selection method are provided.

KEYWORDS:

• Breakdown point
• consistency
• influence function
• nonnegative garrote
• ordinary least-squares estimator
• outliers
• S-estimation
• variable selection

Acknowledgements

The authors thank the editor, an associate editor and two referees for their valuable comments which led to a considerable improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the IAP Research Network IAP P7/06 of the Belgian State (Belgian Science Policy), project GOA/12/014 of the KU Leuven Research Fund, and grant no. Q2 1.5.137.13N of the Flemish Research Foundation (FWO).