Outliers present a major challenge in statistical analysis, especially in regression modeling. While ridge regression is commonly used to manage multicollinearity, it becomes less effective when outliers are involved due to its reliance on least squares estimation. To overcome this issue, Silvapulle,1991 introduced a ridge-type M-estimator specifically designed for handling outliers. Building on this approach, Acitas and Senoglu ,2019 developed a ridge-type estimator based on modified maximum likelihood (MML) estimation, which offers greater robustness against outliers, particularly when the error distribution follows long-tailed symmetry (LTS). This M.Sc. thesis aims to compare the performance of three estimators: the traditional ridge estimator, Silvapulle’s ridge-type M-estimator, and Acitas and Senoglu’s ridge-type MML estimator. The goal is to evaluate these estimators using the mean square error (MSE) criterion through Monte Carlo simulations and real-world datasets. By comparing these methods, the study seeks to identify the best technique for managing outliers and improving the accuracy of regression models. The research includes both a theoretical review and an empirical analysis. The theoretical component involves a comprehensive review of ridge regression, M-estimators, and the ridge-type MML estimator, with a focus on their statistical properties and outlier robustness. The empirical analysis will use Monte Carlo simulations to test the estimators under various conditions of multicollinearity and outlier contamination, as well as apply them to real-world datasets to validate their practical effectiveness. This study is expected to provide insights into the comparative strengths and weaknesses of the traditional ridge estimator, Silvapulle's ridge-type M-estimator, and the ridge-type MML estimator from Acitas and Senoglu. These findings will contribute to the field of robust regression modeling and offer practical value to statisticians, researchers, and practitioners, helping them handle outliers more effectively and improve regression model accuracy.
