A Novel Two-Parameter Estimation Technique for Handling Multicollinearity in Inverse Gaussian Regression Model

This study focuses on the prevalent issue of multicollinearity in the inverse Gaussian regression model (IGRM), which arises when predictor variables have a high degree of correlation. The typical maximum likelihood estimator (MLE) proves to be highly unstable when dealing with linearly linked regressors. Eventually, the accuracy of the model may suffer because of inflated variances and inaccurate coefficient estimates. To improve parameter estimation accuracy and combat multicollinearity, this paper suggests an alternative biased estimator for the IGRM that integrates a two-parameter framework. This novel two-parameter estimator is a general estimator that takes the maximum likelihood, ridge, and Stein estimators as special cases. The theoretical characteristics of the estimator, including its bias and mean squared error (MSE), are develop and then go through a thorough theoretical comparison with the previous estimators in terms of the mean square error matrix (MMSE) criterion. Moreover, the optimal values of the biasing parameters for the advised estimator are also obtained. An extensive simulated study and real-world dataset are examined to assess the practical relevance of the proposed estimator. The empirical results show that, in comparison to conventional estimators, including MLE, ridge, and Stein estimators, the suggested estimator considerably lowers the MSE and improves the parameter estimation accuracy. These results illustrate the novel approach's potential for dealing with multicollinearity in IGRM. The continuous development of reliable estimating methods for generalized linear models (GLMs) is aided by these findings.