Beyond MSE in Poisson Ridge Regression: New Ridge Parameter Estimators with Additional Distributional Performance Criteria

Despite its widespread use for mitigating multicollinearity in count data models, Poisson ridge regression (PRR) remains methodologically constrained by the choice of the ridge parameter k. Existing studies predominantly evaluate ridge parameter estimators using only the mean squared error (MSE) criterion, largely neglecting their distributional properties and estimation stability. Such a narrow evaluation framework may yield unreliable inference, particularly under high correlation and small sample sizes. This study makes two original contributions to the PRR literature. First, we conduct a comprehensive comparison of 13 commonly used ridge parameter estimators and introduce two new estimators that exhibit superior empirical performance. Second, we extend performance evaluation beyond MSE by incorporating outlier ratios and conformity to normality, thereby establishing a multidimensional framework that explicitly addresses distributional robustness and estimator stability. Monte Carlo simulations across 180 scenarios—varying the number of predictors, sample size, correlation level, and intercept value—show that several estimators deemed optimal under MSE perform poorly in terms of outlier prevalence and normality. In contrast, the proposed estimators consistently achieve a balanced performance between error minimization and distributional stability. Two real-data applications further support these findings.