Liu estimation in generalized linear models: application on gamma distributed response variable

Multicollinearity among the explanatory variables seriously effects the maximum likelihood estimator in linear regression models which results in too large estimates in absolute value and in large variance-covariance matrix. The adverse effects of multicollinearity on parameter estimation in generalized linear models are also explored by various authors in the case of maximum likelihood estimation. In this study, we introduce a first-order approximated Liu estimator to combat multicollinearity in generalized linear models which is an extension of the Liu estimator in the linear regression model. We also obtain necessary and sufficient condition for the superiority of the first-order approximated Liu estimator over the the first-order approximated maximum likelihood estimator by the approximated mean squared error criterion. Biasing parameter estimator of the first-order approximated Liu estimator is proposed by minimizing the approximated mean squared error. The results are illustrated by conducting a numerical example and simulation study.