A new effective biased estimator for Poisson regression model under multicollinearity

Count data frequently encountered in various fields are often analyzed using a Poisson regression model (PRM). However, the presence of correlated predictors, known as multicollinearity, poses a challenge to accurately estimating model parameters using a maximum likelihood estimator (MLE). This can lead to unreliable parameter estimates, overestimated variance, and increased mean square error (MSE). To address the problem of multicollinearity in PRM, we propose a new modified Liu-Kibria-Lukman estimator. This estimator combines the advantages of both the adjusted Liu estimator and the Kibria-Lukman estimator. Through extensive Monte Carlo simulations, we rigorously evaluate the performance of our proposed estimator, focussing on the MSE and mean absolute error (MAE) to assess its accuracy in several scenarios. In addition, we present the practical application of our method on an aircraft damage and recreation demand dataset. Both simulation and experimental results demonstrate the superior performance of our proposed estimator in the presence of multicollinearity. Importantly, besides being more accurate, the proposed estimator is very stable and consistent across different datasets and situations. This means it not only lowers errors but also gives results that don't change much when the data or settings vary. This stability makes the estimator more reliable and useful in real-world problems where data can be unpredictable.