New robust ridge estimators for the linear regression model with outliers

Abstract

The ridge regression estimator (RRE) is a widely used estimation method for the multiple linear regression model when the explanatory variables are correlated. The situation becomes problematic for the RRE when the data set contains outliers in the y-direction. The use of the RRE in the presence of outliers may have some adverse effects on parameter estimates. To address this issue, the robust ridge estimators based on M-estimator are available in the literature which are less sensitive to the presence of outliers. It is a well-known fact that the selection of ridge parameter k is very crucial while using the RRE and the same phenomenon may happen in the case of robust ridge estimators. This study proposes some robust ridge estimators for the ridge parameter k. The performance of proposed estimators is evaluated with the help of the Monte Carlo simulations and a real application where the mean squared error (MSE) is considered as a performance evaluation criterion. Results show a better performance of the proposed robust ridge estimators as compared to the RRE, least square and M-estimation methods. While for modified ridge M-estimator, different ridge parameters found to be better for different conditions.

Keywords:

• M-estimator
• Mean squared error
• Multicollinearity
• outlier
• Ridge regression
• Robust ridge M-estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05; 62J07