Adaptive Estimation Strategies in Gamma Regression Model

Abstract

In this study, we considered parameter estimation and inference in the gamma regression model when there exist many covariates, some of which may be treated as a nuisance. We proposed novel estimators based on the pretest and shrinkage strategies and used these to improve the efficiency of estimation. Their asymptotic properties were established. The performance of the proposed estimators was compared with that of the classical estimator through Monte Carlo simulations and application to a real dataset. The pretest and shrinkage estimation strategies were shown to perform well in terms of both parameter estimation and predictive power.