Almost Unbiased Ridge Estimator in the Inverse Gaussian Regression Model

The inverse Gaussian regression (IGR) model is a very common model when the shape of the response variable is positively skewed. The traditional maximum likelihood estimator (MLE) is used to estimate the IGR model parameters. However, when multicollinearity exists among the explanatory variables, the MLE becomes not an efficient estimator as the mean squared error (MSE) becomes inflated. In order to remedy this problem, the ridge estimator (RE) is used. In this paper, we present an almost unbiased ridge estimator for the IGR model in order to overcome multicollinearity problem. We also investigate the performance of the almost unbiased ridge estimator using a Monte Carlo simulation. The results of the almost unbiased ridge estimator are compared with those of the MLE and of the RE in terms of the MSE measure. In addition, a real example of dataset is used and the results show that the performance of the suggested estimator is superior when the multicollinearity is presented among the explanatory variables in the IGR model.