二元逻辑回归模型中的一阶近似刀切Liu估计

A First-Order Approximated Jackknifed Liu Estimator in Binary Logistic Regression Model

摘要: 为了解决二元逻辑回归模型中的复共线性问题，我们结合一阶近似Liu估计和刀切法的优点提出了一个新的估计即一阶近似刀切Liu估计。研究得出了新估计偏差的优良性以及在均方误差矩阵、均方误差准则下优于一阶近似极大似然估计、一阶近似Liu估计和一阶近似刀切岭估计的充要或充分条件。更进一步使用了蒙特卡罗模拟和实证分析来探讨一阶近似刀切Liu估计偏差和在均方误差意义下的优良性。

Abstract: In order to solve the problem of multicollinearity in the binary logistic regression model, we combine the advantages of the first-order approximated Liu estimator and the jackknife procedure, and propose a new estimator, namely the first-order approximated jackknifed Liu estimator. The research obtained the sufficient and necessary or sufficient conditions for the new estimator to be superior to the first-order approximated maximum likelihood estimator, the first-order approximated Liu estimator and the first-order approximated jackknifed ridge estimatior under the bias, mean square error matrix or mean square error criterion. Furthermore, Monte Carlo simulation and empirical analysis are used to explore the first-order approximated jackknifed Liu estimator’s performance in the sense of bias and mean square error.