In this paper, we study the effects of near-singularity which is known as multicollinearity in the binary logistic regression. Furthermore, we also assume the presence of stochastic non-sample linear restrictions. The well-known logistic Liu estimator is combined with the stochastic linear restrictions in order to propose a new method, namely, the stochastic restricted Liu estimation. Theoretical comparisons between the usual maximum likelihood estimator, Liu estimator, stochastic restricted maximum-likelihood estimator and the new stochastic restricted Liu estimator are derived using matrix mean-squared errors of the estimators. A Monte Carlo simulation experiment is designed to evaluate the performances of the listed estimators in terms of mean-squared error and mean absolute error criteria. Artificial data are used to show how to interpret the theorems. According to the results of the simulation, the new method beats the other estimators when the data matrix has the problem of collinearity along with the stochastic restrictions.

中文翻译：

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Logistic回归模型中的随机受限Liu估计量

在本文中，我们研究了近奇异性的影响，即二元逻辑回归中的多重共线性。此外，我们还假设存在随机非样本线性限制。著名的log​​istic Liu估计量与随机线性约束相结合，提出了一种新的方法，即随机约束Liu估计。使用估计量的矩阵均方误差推导出通常的最大似然估计量、Liu 估计量、随机限制最大似然估计量和新的随机限制性 Liu 估计量之间的理论比较。Monte Carlo 模拟实验旨在根据均方误差和平均绝对误差标准评估所列估计器的性能。人工数据用于展示如何解释定理。根据仿真结果，当数据矩阵存在共线性问题和随机限制时，新方法优于其他估计器。