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.

Keywords:

• Inverse Gaussian Regression
• Inverse Gaussian Liu Regression Estimator
• Mean Absolute Error
• Mean Squared Error
• Monte Carlo Simulation

Notes

1 Expected deaths per standard million population

2 United States gallons of absolute alcohol per capita of total population. Consumption figures were taken from “Alcohol Statistics Letters”

3 The proportion of the population living in cities of 25,000 or over.

4 “These findings are also of interest in view of the recurrent emphasis in the literature on a rural-urban discrepancy in rates of alcoholism. Liver cirrhosis death rates are commonly considered to reproduce the prevalence of alcohol abuse in USA and elsewhere, and it may be that what is reported here for mortality from this cause is also true for alcoholism” (see for details, Schmidt, Djur, and Bronetto (1962)).