A Novel Robust Gamma Ridge–Type Regression for Effectively Modeling Multivariate Cancer Data

The gamma regression model (GRM) is widely used for modeling positive, right-skewed continuous data. The maximum-likelihood estimator (MLE) is usually used to estimate the parameters of the GRM. However, two common issues significantly affect the reliability of MLEs: multicollinearity and outliers. Multicollinearity occurs when explanatory variables are highly correlated, which leads to difficulties in interpreting the model parameters, results that are unstable and biased, inflated variance, and an increased mean-squared error; additionally, outliers can cause significant bias and invalid inferences and reduce the model’s efficiency. To solve these issues, we introduce a new robust estimator that can handle both multicollinearity and outliers at the same time in GRM by combining a ridge-type estimator with effective methods like M-estimation and Mallows-type estimators, which results in more accurate and stable outcomes. We explain the statistical features of our new robust estimator and compare it theoretically with other estimators, as well as through Monte Carlo simulations under different conditions. The results indicate that our new estimator consistently performs better than both the standard gamma ridge estimator and other robust gamma ridge estimators when there are outliers and multicollinearity. We also applied our model to a breast cancer dataset in Wisconsin to further validate the scientific utility of the proposed estimator and support the results of the theoretical comparisons and simulations, confirming that our methodology produces more accurate coefficient estimates and better predictions compared to the existing estimators. This provides a robust framework for statisticians when multicollinearity and outliers are common problems.