Abstract It is well known that the use of prior information in the logistic regression improves the estimates of regression coefficients when multicollinearity presents. This prior information may be in the form of exact or stochastic linear restrictions. In this article, in the presence of stochastic linear restrictions, we propose a new efficient estimator, named Stochastic restricted optimal logistic estimator for the parameters in the logistic regression models when the multicollinearity presents. Further, conditions for the superiority of the new optimal estimator over some existing estimators are derived with respect to the mean square error matrix sense. Moreover, a Monte Carlo simulation study and a real data example are provided to illustrate the performance of the proposed optimal estimator in the scalar mean square error sense.

中文翻译：

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最优随机受限逻辑估计量

摘要 众所周知，当存在多重共线性时，在逻辑回归中使用先验信息可以改进回归系数的估计。该先验信息可以采用精确或随机线性限制的形式。在本文中，在存在随机线性限制的情况下，我们针对存在多重共线性时的逻辑回归模型中的参数提出了一种新的有效估计器，称为随机限制最优逻辑估计器。此外，关于均方误差矩阵意义推导出新的最优估计器优于一些现有估计器的条件。此外，还提供了蒙特卡罗模拟研究和真实数据示例，以说明所提出的最优估计器在标量均方误差意义上的性能。