On the performance of some biased estimators in the gamma regression model: simulation and applications

The gamma regression model is widely applied when the response variable is continuous and positively skewed. In the multicollinearity problem, the usual maximum likelihood estimator is inadequate due to its inflated variance. To reduce this effect, well-known ridge and Liu estimators are generally used. In this study, we propose some shrinkage parameters for the new estimator and compared with some best ridge parameters indicated by Amin et al. [Performance of some ridge estimators for the gamma regression model. Stat Pap. 2020;61:997-1026] and two proposed ridge parameters for the GRM specified by Lukman et al. [A new ridge-type estimator for the gamma regression model. Scientifica. 2021;2021:5545356]. A Monte Carlo simulation study and an empirical application are conducted to assess the effectiveness of the proposed and other estimators. Based on the findings of simulation results and applications, we found that one of our proposed estimators performed the best for small dispersion levels.

Automated summary

This study proposes some new shrinkage parameters for the gamma regression model, and demonstrates their superiority in small dispersion levels through empirical comparisons.