New Two Parameter Inverse Gaussian Regression Estimators: Applications and Simulation

Abstract

In situations where the response variable is positively skewed and has an inverse Gaussian distribution, the inverse Gaussian regression (IGR) model is employed. Due to the significant multicollinearity, the variance of the Maximum Likelihood (ML) Estimator is overestimated. In order to tackle multicollinearity in the IGR model, we present a new estimator in this study that combines two parameter estimators. In terms of mean squared error, the suggested estimator’s performance is theoretically compared to that of the
ML and a few other current estimators, as well as through Monte Carlo simulation and various real-data applications. The proposed estimators are found to perform better than the ML, ridge, Liu, Kibria-Lukman, and modified ridge type estimators under several circumstances.

Keywords: Multicollinearity; Inverse Gaussian ridge; Inverse Gaussian Regression model; hybrid estimator; Simulation.