James Stein Estimator for the Inverse Gaussian Regression Model

This paper considers the estimation of parameters for the inverse Gaussian regression model in the presence of multicollinearity. To mitigate this issue, we propose the inverse Gaussian James–Stein estimator (IGJSE) and compare its performance with other estimation methods i.e. maximum likelihood estimator (MLE), ridge and Liu estimators. Theoretical comparisons between the usual MLE, ridge, Liu and IGJSE are derived using matrix mean − squared error and scalar mean squared error criterions. The statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation. The findings of the simulation study clearly demonstrate that the proposed IGJSE showed a consistent behaviour as compared to the other estimation methods in all the evaluated situations. Finally, we evaluate the performance of IGJSE with the help of real example. The simulation and real example results show that the performance of IGJSE is better as compared to other estimation methods with correlated explanatory variables.