A Comparative Study of Robust and Improved Shrinkage Estimators Under Multicollinearity and Outliers Using Multiple Performance Criteria with Application to Health Data

Multicollinearity reduces the reliability of ordinary least squares by increasing variances and creating unstable estimates. This issue has led to biased and penalized regression methods like ridge-, Liu- and Stein-type estimators. Here, we build existing ridge-type approaches by introducing improved ridge and Liu-type estimators, along with robust variants to handle outliers. We investigate their theoretical properties regarding bias, variance, and mean squared error. We also evaluate their performance through Monte Carlo simulations with different levels of multicollinearity and data contamination. By using several evaluation criteria, including mean squared error, akaike information criterion, mean absolute deviation, and mean absolute percentage error, along with an average-rank comparison framework applied here for the first time, we further validate our results with two health-related datasets. The findings show that the strong estimators provide more stable estimates and improved predictive performance, particularly when dealing with severe multicollinearity and outliers.