Performance of ridge estimator in inverse Gaussian regression model

• Published in: Communications in statistics. Theory and methods Vol. 48; no. 15; pp. 3836 - 3849
• Main Author: Yahya Algamal, Zakariya
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03-08-2019; Taylor & Francis Ltd
• Subjects: Chemometrics; Computer simulation; Economic models; inverse Gaussian regression model; Maximum likelihood estimators; Monte Carlo simulation; Multicollinearity; Parameter estimation; Regression models; ridge estimator; shrinkage
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2018.1481977

The presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). Ridge estimator (RE) is a widely used estimator in overcoming this issue. The RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. The inverse Gaussian regression (IGR) model is a well-known model in the application when the response variable positively skewed. The purpose of this paper is to derive the RE of the IGR under multicollinearity problem. In addition, the performance of this estimator is investigated under numerous methods for estimating the ridge parameter. Monte Carlo simulation results indicate that the suggested 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.