Abstract

In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

摘要

在众多应用领域中，当响应变量是连续的、正偏态的并且很好地拟合逆高斯分布时，逆高斯回归模型 (IGRM) 是这种情况下的有效方法。多重共线性问题在化学计量学、生物学、金融学等多个应用领域中非常普遍。使用岭估计器可以减少多重共线性的影响。本研究提出了新的岭估计器来解决 IGRM 中的多重共线性问题。将新估计器的性能与最大似然估计器和其他一些现有估计器进行比较。均方误差用作性能评价标准。进行蒙特卡罗模拟研究以评估基于最小均方误差标准的新岭估计器的性能。蒙特卡罗模拟结果表明，所提出的估计器的性能优于现有方法。还使用两个真实的化学计量学应用评估了所提出的岭估计器的比较。蒙特卡罗模拟和实际应用的结果证实了所提出的岭估计器优于其他竞争方法。