A new improved Liu estimator for the QSAR model with inverse Gaussian response

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions.