A restricted gamma ridge regression estimator combining the gamma ridge regression and the restricted maximum likelihood methods of estimation

In this article, we propose a restricted gamma ridge regression estimator (RGRRE) by combining the gamma ridge regression (GRR) and restricted maximum likelihood estimator (RMLE) to combat multicollinearity problem for estimating the parameter beta in the gamma regression model. The properties of the new estimator are discussed, and its superiority over the GRR, RMLE and traditional maximum likelihood estimator is theoretically analysed under different conditions. We also suggest some estimating methods to find the optimal value of the shrinkage parameter. A Monte Carlo simulation study is conducted to judge the performance of the proposed estimator. Finally, an empirical application is analysed to show the benefit of RGRRE over the existing estimators.

Automated summary

This article introduces a restricted gamma ridge regression estimator (RGRRE) to address multicollinearity issues in estimating the parameter beta in the gamma regression model. The properties and superiority of the new estimator are theoretically analyzed, along with suggested methods for finding the optimal shrinkage parameter value. Monte Carlo simulation and empirical application demonstrate the benefits of RGRRE over existing estimators.