二元逻辑回归模型中的随机约束两参数极大似然估计

Stochastic Restricted Two-Parameter Maximum Likelihood Estimator in Binary Logistic Regression Model

摘要: 针对二元逻辑回归模型中的复共线性问题，同时考虑模型中待估参数存在先验信息的情况，提出了一类新估计即随机约束两参数极大似然估计。研究得到了新估计在均方误差矩阵准则下优于Liu极大似然估计，Liu-Type极大似然估计，两参数极大似然估计，随机约束极大似然估计，随机约束Liu极大似然估计和随机约束Liu-Type极大似然估计的充要或充分条件。探讨并给出了新估计中偏参数的最优建议值。更进一步，基于偏参数的最优建议值，通过蒙特卡罗模拟方法，分析了新估计在均方误差意义下的优良性。

Abstract: To solve the multicollinearity problem in binary logistic regression model, a new estimator, namely stochastic restricted two-parameter maximum likelihood estimator, is proposed, considering the existence of prior information of the parameters to be estimated in the model. Moreover, we obtain the necessary or sufficient conditions for the new estimator to be superior to Liu maximum likelihood estimator, Liu-Type maximum likelihood estimator, two-parameter maximum likelihood estimator, stochastic restricted maximum likelihood estimator, stochastic restricted Liu maximum likelihood estimator and stochastic restricted Liu-Type maximum likelihood estimator under the criterion of mean squared error matrix. The recommend optimal values of the biasing parameters in the new estimation are discussed and given. Furthermore, based on the optimal recommended value of biasing parameters, a Monte Carlo simulation experiment is introduced to discuss the performance of this new estimator under the mean squared error.

文章引用：邹媛, 陈景, 李荣. 二元逻辑回归模型中的随机约束两参数极大似然估计[J]. 统计学与应用, 2020, 9(4): 515-524. https://doi.org/10.12677/SA.2020.94055

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