ON SOME NEW RIDGE M-ESTIMATORS FOR LINEAR REGRESSION MODELS UNDER VARIOUS ERROR DISTRIBUTIONS.

Ridge regression is used to circumvent the problem of multicollinearity in the multiple linear regression models. Beside the multicollinearity, when the outliers in the y-direction are also present, then the usual ridge regression estimators gives inefficient results in terms of mean squared error (MSE). In order to mitigate such situation, ridge M-estimators are often used. Several estimators are available in literature but they do not perform well in terms of MSE when the joint problem of high multicollinearity and y-direction outliers is present. In this article, some new quantile based ridge M-estimators are proposed. The new estimators are then compared with other existing estimators through extensive Monte Carlo simulations for various error term distributions, degrees of multicollinearity and percentage of y-direction outliers. Based on simulation study with minimum MSE criterion, the new estimators outperform in many considered scenarios. Particularly, in case of high multicollinearity, y-direction outliers and heavy tailed error distributions, the proposed estimators have shown efficient results. A numerical example is also presented to support the simulation results. [ABSTRACT FROM AUTHOR]