New robust estimator for handling outliers and multicollinearity in gamma regression model with application to breast cancer data.

The gamma regression model (GRM) is commonly used to analyze continuous data that are positively skewed. However, the GRM is sensitive to multicollinearity and outliers. These two problems often occur in regression analysis. Multicollinearity can make the estimated coefficients unstable and cause inflated variance, while outliers can lead to misleading results and reduce the reliability of statistical conclusions. To overcome these issues, we propose a new robust gamma ridge regression estimator that combines a ridge regression estimator with robust estimation methods such as M-estimation and Mallows-type estimators. The ridge part of the model helps to reduce the effects of multicollinearity, while the robust estimation minimizes the impact of outliers, leading to more accurate and stable results. We support our method with detailed theoretical comparisons and a series of Monte Carlo simulations under different conditions. The results show that our proposed model consistently performs better than the traditional gamma ridge regression estimator, especially when multicollinearity and outliers are present. Furthermore, we apply our model to a breast cancer dataset that contains both issues. The application confirms that our method provides more reliable coefficient estimates and better predictions compared to the conventional methods. Based on these results, we recommend using this robust gamma ridge regression estimator, especially in biomedical studies and other fields where multicollinearity and outliers are common problems.