Improved robust ridge M-estimation

ABSTRACT

It is developed that non-sample prior information about regression vector-parameter, usually in the form of constraints, improves the risk performance of the ordinary least squares estimator (OLSE) when it is shrunken. However, in practice, it may happen that both multicollinearity and outliers exist simultaneously in the data. In such a situation, the use of robust ridge estimator is suggested to overcome the undesirable effects of the OLSE. In this article, some prior information in the form of constraints is employed to improve the performance of this estimator in the multiple regression model. In this regard, shrinkage ridge robust estimators are defined. Advantages of the proposed estimators over the usual robust ridge estimator are also investigated using Monte-Carlo simulation as well as a real data example.

KEYWORDS:

• M-estimation
• multicollinearity
• non-sample information
• outliers
• ridge regression
• shrinkage

AMS CLASSIFICATION:

• 62J07
• 62F35

Acknowledgments

The authors gratefully acknowledge the helpful comments and suggestions of the reviewer, that have improved this paper. Thanks are due to the editor and referees for their valuable input while reading the manuscript, which resulted in the present form. Professor S. E. Ahmed was supported by the grant from NSREC.

Disclosure statement

No potential conflict of interest was reported by the authors.