New shrinkage parameters for the inverse Gaussian Liu regression

Abstract

In the Inverse Gaussian Regression (IGR), there is a significant increase in the variance of the commonly used Maximum Likelihood (ML) estimator in the presence of multicollinearity. Alternatively, we suggested the Liu Estimator (LE) for the IGR that is the generalization of Liu. In addition, some estimation methods are proposed to estimate the optimal value of the Liu shrinkage parameter, d. We investigate the performance of these methods by means of Monte Carlo Simulation and a real-life application where Mean Squared Error (MSE) and Mean Absolute Error (MAE) are considered as performance criteria. Simulation and application results show the superiority of new shrinkage parameters to the ML estimator under certain condition.