Abstract

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 Genç method for the IGRM is better than the other competitive estimators.

摘要

逆高斯回归模型 (IGRM) 经常应用于响应变量呈正偏态并很好地拟合逆高斯分布的情况。最大似然估计器 (MLE) 通常用于估计 IGRM 的未知回归系数。如果解释变量彼此不相关，则 MLE 方法的性能更好。但是多重共线性的存在通常会夸大 MLE 的方差和标准误差，从而导致估计效率的损失。因此，对于 IGRM 的未知回归系数的估计，MLE 不是一个值得信赖的方法。为了对抗多重共线性，我们为 IGRM 提出了两个参数估计器 (TPE)，以提高估计的效率。而且，均方误差准则被考虑在内，以比较 TPE 与其他有偏估计器和 MLE 的性能，使用蒙特卡罗模拟研究和一个真实的例子。基于蒙特卡罗模拟研究的结果和一个真实的例子，我们可以建议基于 Asar 和 Genç 方法的 IGRM 的 TPE 优于其他竞争估计器。