In this study, the effects of multicollinearity on the maximum likelihood estimator are analyzed in the probit regression model. It is known that the near-linear dependencies in the design matrix affect the maximum likelihood estimation negatively, namely, the standard errors become so large so that the estimations are said to be inconsistent. Therefore, a new jackknifed ridge estimator is introduced as an alternative to the maximum likelihood technique and the well-known ridge estimator. The mean squared error properties of the listed estimators are investigated theoretically. In order to evaluate the performance of the estimators, a Monte Carlo simulation study is designed, and simulated mean squared error and squared bias are used as performance criteria. Finally, the benefits of the new estimator are illustrated via a real data application.

中文翻译：

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概率回归模型中的折刀岭估计器

本研究在概率回归模型中分析了多重共线性对最大似然估计量的影响。众所周知，设计矩阵中的近线性相关性对最大似然估计产生负面影响，即标准误差变得如此之大，以至于估计被称为不一致。因此，引入了新的 jackknifed 脊估计器作为最大似然技术和众所周知的脊估计器的替代方法。从理论上研究了所列估计量的均方误差特性。为了评估估计器的性能，设计了蒙特卡罗模拟研究，并使用模拟均方误差和平方偏差作为性能标准。最后，通过实际数据应用程序说明了新估算器的好处。