Robust Lasso Estimator for the Liu-Type regression model and its applications

In this paper, we propose a new estimator for Liu-Type regression model, called the LAD-Lasso-Liu estimator, which addresses the issues of multicollinearity, outliers and it performs the variable selection. By combining the LAD Lasso and Liu-Type estimators, our proposed estimator achieves double shrinkage for the parameters and at the same time it has the robust properties. We thoroughly discuss the properties of the new estimator and conduct a simulation study to demonstrate its superiority over the LAD, Lasso, and LAD-Lasso estimators. We used the Median(MSE) as a criteria to compare between the estimators at a different factors. The simulation results showed that the proposed estimator has superiority over the other estimators especially when the correlation coefficient between the explanatory variables increases and when the error variance decreases. In addition, the proposed estimator has better correct selection of the number of zeros coefficients than other penalized estimators. To demonstrate the work of the estimator presented under empirical data, we apply the proposed estimator to prostate cancer data. Our results for the empirical data indicate that the proposed estimator outperforms the other estimators and can provide accurate results in challenging scenarios with multicollinearity and outliers.