On some ridge regression estimators: a nonparametric approach

Abstract

This paper considers the R-estimation of the parameters of a multiple regression model when the design matrix is ill-conditioned. Accordingly, we introduce the ridge regression (RR) modification to the usual R-estimators and consider five RR R-estimators when it is suspected that the regression parameters may belong to a linear subspace of the parameter space. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Asymptotic relative efficiency tables and risk graphs are provided for the numerical and graphical comparisons of the five estimators.

Keywords:

• dominance
• linear regression model
• nonparametric methods
• preliminary test
• relative efficiency
• ridge regression
• R-Estimation
• Shrinkage estimation

AMS 2010 Subject Classifications:

• 62G08
• 62G05
• 62G20

Acknowledgements

The authors are thankful to the Associate Editor and referee for their valuable comments and suggestions which certainly improved the quality and presentation of the paper. This research was supported by the Discovery Grant from NSERC of the first author. This paper was written while the second author was on sabbatical leave (2010–2011). He is grateful to Florida International University for awarding him the sabbatical leave which, gave him excellent research facilities.