New robust two-parameter estimator for overcoming outliers and multicollinearity in Poisson regression model

The Poisson maximum likelihood estimator (PMLE) is commonly used to estimate the coefficients of the Poisson regression model (PRM). However, it is well known that the PMLE is highly sensitive to outliers, which can distort the estimated coefficients and lead to misleading results. Different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PMLE is sensitive to multicollinearity, since multicollinearity leads to an inflation of the variance, an error in the signals of the coefficients, as well as an increase in the mean squared error (MSE) value. Therefore, several biased Poisson estimators have been provided to handle this problem, such as the Poisson ridge estimator and the Poisson modified ridge-type estimator. Despite different Poisson-biased regression estimators being proposed, there has been no analysis of the robust version of these estimators to deal with the two above-mentioned problems simultaneously, except for minimal work. This paper proposed a new robust Poisson two-parameter estimator (PMT-PTE), which combines the transformed M-estimator (MT) with the two-parameter estimator, providing a new approach to handling outliers and multicollinearity. Theoretical comparisons and Monte Carlo simulations were conducted to show the proposed performance compared with the other estimators. The simulation results indicated that the proposed PMT-PTE estimator outperformed the other estimators in different scenarios, in cases where both problems existed. Finally, we analyzed a real-world dataset that encompasses both problems, and the results confirmed the theoretical and simulation results and demonstrated the superiority of the proposed estimator, introducing a new approach to data analysis.