Generalized Two Parameter Estimator in Inverse Gaussian Regression Model

Abstract

This article introduces generalized two-parameter estimators for modelling explanatory variables in positively skewed data using the inverse Gaussian regression model. The standard approach for estimating unknown regression coefficients relies on the maximum likelihood method. Although the maximum likelihood estimator is a powerful estimation tool, its performance can be severely affected by multicollinearity among explanatory variables. When these variables are correlated, the variances and standard errors inflate, reducing estimator precision. As a result, the maximum likelihood estimator becomes unreliable for estimating regression coefficients. Similarly, in the presence of strong multicollinearity, the Ordinary Least Squares estimator also yields misleading results. In this paper, we propose a new estimator and compare it with existing methods, including the Ordinary Least Squares estimator, Ridge Regression estimator, Liu estimator, and Two-Parameter estimator. The discussion further addresses the estimation of biased parameters and examines the necessary and sufficient conditions associated with the proposed approach. We evaluate the performance of the new estimator using the matrix mean squared error criterion and a simulation study that considers various sample sizes, degrees of multicollinearity, parameter settings, and variance levels. To illustrate practical applicability, we analyze the Theoph dataset, demonstrating that the proposed estimator performs more efficiently than the maximum likelihood estimator and other established techniques. The results show that the generalized two-parameter estimators achieve lower mean squared error than maximum likelihood estimators and deliver superior performance compared to existing methods.