Hadi Emami

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.

Semi‌parametric linear models have gained significant attention from researchers because of their unique characteristics, which combine elements of both fully parametric and nonparametric models. By leveraging the strengths of both types of models, these models offer more precise and flexible regression analyses. When fitting any model, including semi‌parametric regression models, researchers may not have complete information on the variables and may encounter the issue of censoring. If the response variable is censored for some of the observations, the parameter estimates obtained using conventional regression methods will be biased. In this thesis, a suitable estimation method for parameters in semi-parametric regression models in the presence of censored data is proposed. In addition to censored data, collinearity among the explanatory variables presents another challenge for semi‌parametric regression models. Collinearity is problematic, and its impact on various aspects of regression models is well documented. These effects include variance inflation, incorrect signs of regression estimates, and the invalidity of important variables. In this context, the use of ridge estimators is proposed to address collinearity in censored semi‌parametric linear models. Researchers have provided substantial evidence of outliers and their detrimental effects on the parameter estimates of regression models. The utilization of least trimmed squares estimators, a powerful method for regression analysis in the presence of outliers, has been suggested. By mitigating the influence of outliers, this method can yield more reliable and stable results. Generalizing these estimators is one of the commonly employed estimation methods due to their simplicity, high breakdown point, and robustness against outliers. In this thesis, the least trimmed squares and ridge estimators are extended to censored semi‌parametric regression models in the presence of outliers. Further‌ more, the proposed estimators are compared to conventional estimators using Monte Carlo simulation results, and finally, these estimators are applied to a real‌ world dataset.