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The ordinary least squared and ridge regression estimators in a linear regression model are sensitive to outliers in the y-variable. In such situations, ridge M-estimators are widely used which are robust to the y-variable outliers and overcome the multicollinearity problem. Similar to ridge regression, to lower the mean square error (MSE) of ridge M-estimators, it is crucial to select the most robust ridge parameter. The performance of existing estimators for the estimation of robust ridge parameters deteriorates when the degree of multicollinearity, error variance, and y-variable outliers increases from moderate to high. In this paper, some new robust ridge M-estimators have been proposed. The efficiency of the new estimators has been compared through a Monte Carlo simulation study. Based on the MSE criterion, the new estimators outperform existing estimators. A numerical example has been provided to illustrate the simulation results.

Modified robust ridge M-estimators for linear regression models: an application to tobacco data