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

Abstract

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.

KEYWORDS:

• Biased estimator
• generalized linear model
• GRM
• Liu estimator
• maximum likelihood estimator
• mean squared error
• multicollinearity
• ridge estimator
• shrinkage estimators
• simulation study

2010 MATHEMATICAL SUBJECT CLASSIFICATIONS:

• 62J07
• 62J12

Disclosure statement

No potential conflict of interest was reported by the author(s).