Robust Estimation in Ridge Regression
Project no. 23337 · Status: Kapanmış (Yayın bekleniyor) · 2021
Summary
<p>In this study, ridge regression is employed to mitigate the impact of multicollinearity, while robust estimation methods are utilized to alleviate the influence of outliers. These two issues are addressed simultaneously, leading to the proposal of a new robust ridge regression estimator. The aim of the thesis is to propose a regression estimator that remains unaffected by outliers and is more effective than the others. By adapting this estimator to the ridge regression format, the objective is to obtain a robust ridge regression estimator that is impervious to the multicollinearity problem, exhibits high efficiency, and maintains robustness.</p><p> In the study, Dynamically Weighted Modified Maximum Likelihood (DWMML) robust regression estimators are derived using the philosophy of DWMML robust estimators as proposed in Sazak's (2019) study. Subsequently, DWMML regression estimators are adapted to ridge regression, resulting in the development of new robust ridge regression estimators, termed Dynamically Weighted Modified Maximum Likelihood Ridge (DWMMLR) estimators.</p><p>DWMMLR estimators yield nearly optimal results, closely approaching the efficiency performance of the Least Squares (LS) Ridge estimators, even under normal distribution assumptions. Additionally, it has been observed that the DWMMLR3 estimators outperform other robust ridge regression estimators in various conditions.</p>