New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

The Poisson maximum likelihood (PML) is used to estimate the coefficients of regression model (PRM). Since resulting estimators are sensitive outliers, different studies have provided robust alleviate this problem. Additionally, PML estimator multicollinearity. Therefore, several biased been cope with problem, such as ridge estimator, Liu Kibria–Lukman and modified estimator. Despite being proposed, there has no analysis version these deal two above-mentioned problems simultaneously, except for which we extended by proposing three new one-parameter estimators, namely, (RPL), (RPKL), (RPMKL). Theoretical comparisons Monte Carlo simulations were conducted show proposed performance compared other estimators. simulation results indicated that RPL, RPKL, RPMKL outperformed in scenarios, cases where both existed. Finally, analyzed real datasets confirm results.