Abstract

Multi-collinearity among regressors and consequently ill-conditioning inflates the mean squared error (MSE) of the maximum likelihood estimator (MLE) of the parameters in a regression model. In recent years, the Liu estimator (LE) has been widely used in the literature to improve the regression models. Since in some regression models, the dependent variable follows a double bounded distribution, such as the beta and Kumaraswamy distributions, we are going to consider these two regression models in the presence of a multi-collinearity problem with investigation of their properties, characterizations, MLEs, and LEs. Finally, MSEs of LEs and MLEs are compared under various link functions, using simulation and two real data sets.

摘要

回归变量之间的多重共线性和因此的病态会扩大回归模型中参数的最大似然估计 (MLE) 的均方误差 (MSE)。近年来，刘估计量（LE）在文献中被广泛用于改进回归模型。由于在某些回归模型中，因变量遵循双重有界分布，例如 beta 和 Kumaraswamy 分布，我们将在存在多重共线性问题的情况下考虑这两个回归模型，并研究它们的属性、表征、MLE , 和 LE。最后，使用仿真和两个真实数据集比较了 LE 和 MLE 在各种链接函数下的 MSE。