A new two-parameter estimator for the inverse Gaussian regression model with application in chemometrics

The presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). The inverse Gaussian regression (IGR) model is a well-known model in application when the response variable positively skewed. To address the problem of multicollinearity, a two-parameter estimator is proposed (TPE). The TPE enjoys the advantage that its mean squared error (MSE) is less than MLE. The TPE is derived and the performance of this estimator is investigated under several conditions. Monte Carlo simulation results indicate that the proposed estimator performs better than the MLE estimator in terms of MSE. Furthermore, a real chemometrics dataset application is utilized and the results demonstrate the excellent performance of the suggested estimator when the multicollinearity is present in IGR model.