In this research, we propose a novel regression estimator as an alternative to the Liu estimator for addressing multicollinearity in the Bell regression model, referred to as the almost unbiased Liu estimator. Moreover, the theoretical characteristics of the proposed estimator are analyzed, along with several theorems that specify the conditions under which the almost unbiased Liu estimator outperforms its alternatives. A comprehensive simulation
study is conducted to demonstrate the superiority of the almost unbiased Liu estimator and to compare it against the Bell Liu estimator and the maximum likelihood estimator. The practical applicability and advantage of the proposed regression estimator are illustrated through a real-world dataset. The results from both the simulation study and the real-world data application indicate that the new almost unbiased Liu regression estimator outperforms its counterparts based on the mean square error criterion