Estimating the Unrestricted and Restricted Liu Estimators for the Poisson Regression Model: Method and Application

This paper considers both unrestricted and restricted Liu estimators in the presence of multicollinearity for the Poisson regression model. It also considers some new estimators of the shrinkage parameter for both unrestricted and restricted Liu estimators. Based on a simulation study and its empirical application, we found that the restricted estimator outperforms the unrestricted one. Further, the restricted Liu estimator also outperforms both the unrestricted Liu and restricted Liu estimators. Hence, this new method is a preferred option when the coefficient vector beta may belong to a linear sub-space defined byR beta = r.

Automated summary

This paper explores both unrestricted and restricted Liu estimators in the context of multicollinearity in the Poisson regression model, introducing new estimators for the shrinkage parameter. Through simulation and empirical application, it is found that the restricted estimator outperforms the unrestricted one, with the restricted Liu estimator showing superior performance to both the unrestricted Liu and restricted Liu estimators. This new method is therefore preferred when the coefficient vector may belong to a linear sub-space.