Modified ridge-type estimator for the inverse Gaussian regression model

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated.