Two-parameter estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is frequently applied in the situations, when the response variable is positively skewed and well fitted to the inverse Gaussian distribution. The maximum likelihood estimator (MLE) is generally used to estimate the unknown regression coefficients of the IGRM. The performance of the MLE method is better if the explanatory variables are uncorrelated with each other. But the presence of multicollinearity generally inflates the variance and standard error of the MLE resulting the loss of efficiency of estimates. So, for the estimation of unknown regression coefficients of the IGRM, the MLE is not a trustworthy method. To combat multicollinearity, we propose two parameter estimators (TPE) for the IGRM to improve the efficiency of estimates. Moreover, mean squared error criterion is taken into account to compare the performance of TPE with other biased estimators and MLE using Monte Carlo simulation study and a real example. Based on the results of Monte Carlo simulation study and a real example, we may suggest that the TPE based on Asar and Genc method for the IGRM is better than the other competitive estimators.