An unbiased ridge estimator for the poisson regression model: Method, simulation, and application to plywood quality

The Poisson model is a commonly used model for analyzing count data in regression. The Poisson maximum likelihood (PML) estimator is used to estimate the regression parameters of the model. Such the PML is affected by multicollinearity problems, then biased estimators have been developed to address this problem, such as the Poisson ridge (PR) estimator. Even though the PR estimator reduces the effect of multicollinearity problems in the model, it increases the bias in estimation. So, recently, some estimators have been proposed to reduce this bias, such as the Jackknifed Poisson ridge (JPR) and modified Jackknifed Poisson ridge (MJPR) estimators. These estimators have two advantages: firstly, they reduce the effect of multicollinearity, and secondly, they decrease the bias and consequently improve their performance. To remove the effect of bias from the estimator, we introduce an unbiased Poisson ridge (UPR) estimator by analogy with the unbiased ridge estimator. We derive the properties of the UPR estimator. We compare the proposed estimator (UPR) with other existing estimators (PML, PR, JPR, and MJPR) theoretically using the mean square error matrix as a measure of goodness of fit. Furthermore, a simulation study and real-life application have been provided to support the theoretical findings.