Developing a Liu estimator for the negative binomial regression model: method and application

This paper introduces a new shrinkage estimator for the negative binomial regression model that is a generalization of the estimator proposed for the linear regression model by Liu [A new class of biased estimate in linear regression, Comm. Stat. Theor. Meth. 22 (1993), pp. 393–402]. This shrinkage estimator is proposed in order to solve the problem of an inflated mean squared error of the classical maximum likelihood (ML) method in the presence of multicollinearity. Furthermore, the paper presents some methods of estimating the shrinkage parameter. By means of Monte Carlo simulations, it is shown that if the Liu estimator is applied with these shrinkage parameters, it always outperforms ML. The benefit of the new estimation method is also illustrated in an empirical application. Finally, based on the results from the simulation study and the empirical application, a recommendation regarding which estimator of the shrinkage parameter that should be used is given.