Performance of Liu-Type Estimator in Inverse Gaussian Regression Model

Abstract

The ridge regression model has been shown to be an effective shrinking strategy for reducing the impacts of multicollinearity on a number of occasions. When the response variable is positively skewed, the inverse Gaussian regression model (IGR) is a popular model to use. Multicollinearity, on the other hand, is known to reduce the variance of the maximum likelihood estimator of inverse Gaussian regression coefficients. A novel estimator is proposed in this paper by presenting a generalization of the Liu-type estimator using inverse Gaussian regression (NIGLTE). The performance of NIGLTE is fully depending on the shrinkage parameter, k. In this paper, three selection methods of the shrinkage parameter are explored and investigated. In addition, their predictive performances are considered. Our Monte Carlo simulation and real application results suggest that some estimators can bring significant improvement relative to others, in terms of mean squared error.