Shrinkage estimators for gamma regression model

Abstract

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a well-known model in application when the response variable positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model (GRRM) has been proposed. The performance of GRRM is fully depending on the shrinkage parameter. In this paper, numerous selection methods of the shrinkage parameter are explored and investigated. In addition, their predictive performances are considered. Our Monte Carlo simulation results suggest that some estimators can bring significant improvement relative to others, in terms of mean squared error and prediction mean squared error.