Principal component ridge type estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is applied when the response variable y is continuous, positively skewed and well fitted to the inverse Gaussian distribution. In the presence of multicollinearity, the maximum likelihood estimation (MLE) is not a right choice. Therefore, we proposed a new estimator called the principal component ridge estimator for the IGRM which combines the principal component estimator and the ridge estimator. We also consider a two-parameter estimator (TPE) and other biased estimators to see a clear image of our proposed estimator. A Monte Carlo simulation study is also presented to examine the performance of the proposed estimators. Furthermore, we analysed a dataset to assess the superiority of the proposed estimator. Based on the simulation and application results, it is evident that the proposed estimator dominates the classical MLE, and other considered biased estimation methods.

Automated summary

This article introduces the inverse Gaussian regression model and proposes a principal component ridge estimator for the model in the presence of multicollinearity. Through Monte Carlo simulation study and analysis of a real dataset, it is demonstrated that the proposed estimator outperforms the classical MLE and other biased estimation methods.