New robust ridge-type estimators for beta regression under multicollinearity and outliers with application to breast cancer data

The beta regression model (BRM) is a widely applied modeling approach for data bounded within the open interval (0, 1), and it is extensively used in fields such as chemistry, environmental science, medicine, and biology. Parameter estimation in these models is conventionally performed using the maximum likelihood estimator (MLE). However, the MLE is known to be sensitive to multicollinearity among predictors and the presence of outliers, which can bias coefficient estimates, inflate their variance, and increase the mean squared error (MSE), potentially leading to erroneous inferences. To address these issues, this paper introduces new robust biased estimators for BRM that are named robust ridge-type estimators. These estimators are designed to handle the adverse effects of multicollinearity and outliers. We used a theoretical comparison to compare the proposed estimators against the MLE and existing robust ridge estimators. Furthermore, a simulation study was performed under different conditions to evaluate the performance of the proposed estimators. Both the theoretical comparison and simulation results demonstrate the superior performance of the proposed estimators in the presence of multicollinearity and outliers. The practical utility of the methods was further validated through an application to a real-world dataset on breast cancer data. The results confirm that the proposed estimators provide greater reliability and robustness compared to existing methods. These results emphasize the importance of using robust biased estimation techniques to enhance the accuracy and reliability of regression models, especially in empirical research involving multicollinear and outlier data.