A new shrinkage estimator in negative binomial regression model

Abstract

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The negative binomial regression model (NBRM) is a well-known model in application when the response variable is a count data with overdispersion. However, it is known that the variance of maximum likelihood estimator (MLE) of the NBRM coefficients can negatively affected in the presence of multicollinearity. In this paper, the generalized ridge estimator is proposed to overcome the limitation of ridge estimator. Several methods for estimating the shrinkage matrix have been adapted. Our Monte Carlo simulation results suggest that the proposed estimator, regardless the type of estimating method of shrinkage matrix is better than the MLE estimator and ridge estimator, in terms of MSE. In addition, some estimating method of shrinkage matrix can bring significant improvement relative to others.