Abstract

In the Inverse Gaussian Regression (IGR), there is a significant increase in the variance of the commonly used Maximum Likelihood (ML) estimator in the presence of multicollinearity. Alternatively, we suggested the Liu Estimator (LE) for the IGR that is the generalization of Liu. In addition, some estimation methods are proposed to estimate the optimal value of the Liu shrinkage parameter, d. We investigate the performance of these methods by means of Monte Carlo Simulation and a real-life application where Mean Squared Error (MSE) and Mean Absolute Error (MAE) are considered as performance criteria. Simulation and application results show the superiority of new shrinkage parameters to the ML estimator under certain condition.

摘要

在逆高斯回归 (IGR) 中，在存在多重共线性的情况下，常用的最大似然 (ML) 估计量的方差显着增加。或者，我们建议 IGR 的 Liu Estimator (LE) 是 Liu 的概括。此外，还提出了一些估计方法来估计 Liu 收缩参数d的最优值。我们通过蒙特卡罗模拟和实际应用来研究这些方法的性能，其中均方误差 (MSE) 和平均绝对误差 (MAE) 被视为性能标准。仿真和应用结果表明，在一定条件下，新的收缩参数对 ML 估计器的优越性。