Almost unbiased ridge estimator in Bell regression model: theory and application to plastic polywood data

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion.