Logistic Regression is a very popular method to model the dichotomous data. The maximum likelihood estimator (MLE) of unknown regression parameters of the logistic regression is not too accurate when multicollinearity exists among the covariates. It is well known that the presence of multicollinearity increases the variance of the MLE. To diminish the inflated mean square error (MSE) of the MLE due to the presence of multicollinearity, we proposed a new estimator designated as linearized ridge logistic estimator. The conditional superiority of the proposed estimator over the other existing estimators is derived theoretically and the optimal choice of shrinkage parameter is suggested. Monte Carlo simulations are performed to study the performance of the proposed estimator through MSE sense. Also, a numerical example is presented to support the results.

中文翻译：

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多重共线性存在下的线性岭对数估计

Logistic回归是一种非常受欢迎的建模二分数据的方法。当协变量之间存在多重共线性时，逻辑回归的未知回归参数的最大似然估计器（MLE）不太准确。众所周知，多重共线性的存在增加了MLE的方差。为了减少由于多重共线性而导致的MLE膨胀均方误差（MSE），我们提出了一种新的估计器，称为线性脊对数估计器。理论上推导了所提出的估计量相对于其他现有估计量的条件优越性，并提出了收缩参数的最佳选择。进行了蒙特卡洛（Monte Carlo）仿真，以通过MSE感觉来研究所提出的估计器的性能。也，