This study delves into the intricacies of addressing multicollinearity and outliers in Poisson regression modeling. Our examination encompasses a comprehensive survey of well-established methodologies, such as the ridge estimator and MT-estimator, and recent innovations like the enhanced ridge-type estimator. These approaches bolstered the robust estimation of the Poisson regression modeling with the development of a robust method. Through a series of numerical studies, including simulations and a meticulous analysis of the English League Football data, we empirically validate the efficacy of these methods. This research contributes to the evolving toolkit for effectively handling count data in the dynamic field of statistics.

Summary The method of maximum likelihood flops when there is linear dependency (multicollinearity) and outlier in the generalized linear models. In this study, we combined the ridge estimator with the transformed M‐estimator (MT) and the conditionally unbiased bounded influence estimator (CE). The two new estimators are called the robust MT estimator and Robust‐CE. A Monte Carlo study revealed that the proposed estimators dominate for the generalized linear models with Poisson response and log link function. The real‐life application results support the simulation outcome.

Abstract This study introduces a new biased estimator called the K‐L estimator for the linear mixed model to overcome the effect of multicollinearity. We derived the mean squared error property of the proposed estimator and made a theoretical comparison with other methods. For the assessment of the K‐L estimator, we use the mean squared error criterion as a performance evaluation criterion. Moreover, we defined some shrinkage parameters for the proposed estimator. For numerical evaluation, we use a Monte Carlo simulation study and a real example. The result shows the supremacy of the K‐L estimator as compared to the available methods under certain conditions.

Abstract Multicollinearity poses an undesirable effect on the efficiency of the maximum likelihood estimator (MLE) in both Gaussian and non‐Gaussian regression models. The ridge and the Liu estimators have been developed as an alternative to the MLE. Both estimators possess smaller mean squared error (MSE) over the MLE. Recently, Kibria and Lukman developed KL estimator, which was found to outperform the ridge and the Liu estimators in the linear regression model. With this expectation, we developed the KL estimator for the inverse Gaussian regression model. We compare the proposed estimator's performance with some existing estimators in terms of theoretical comparison, the simulation study, and real‐life application. Smaller MSE criterion shows that the proposed estimator with one of its shrinkage parameter performs the best.