A modified Liu estimator for the Inverse Gaussian Regression Model
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Abstract
Multicollinearity poses an undesirable effect on the efficiency of the maximum likelihood estimator (MLE) in Inverse Gaussian Regression Model (IGRM). The Inverse Gaussian Regression Model (IGRM) is used when the response variable is positively skewed and follows an inverse Gaussian distribution. To mitigate this problem, The ridge and the Liu estimators have been developed as an alternative to the MLE. Both estimators possess smaller mean squared error (MSE) over the MLE. the drawback of using the traditional Liu estimator is that in most of the times, the shrinkage parameter d, attains a negative value which is the major disadvantage of traditional Liu estimator. So, to overcome this problem, we propose a new adjusted Inverse Gaussian Liu estimator (MIGLE) for the (IGRM) which is the robust solution to the problem of multicollinear explanatory variables. We compare the proposed estimator’s performance with some existing estimators in the simulation study, and real-life application. Smaller mean squared error MSE criterion shows that the proposed estimator with one of its shrinkage parameters performs the best.
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