Poisson regression is a very commonly used technique for modeling the count data in applied sciences, in which the model parameters are usually estimated by the maximum likelihood method. However, the presence of multicollinearity inflates the variance of maximum likelihood (ML) estimator and the estimated parameters give unstable results. In this article, a new linearized ridge Poisson estimator is introduced to deal with the problem of multicollinearity. Based on the asymptotic properties of ML estimator, the bias, covariance and mean squared error of the proposed estimator are obtained and the optimal choice of shrinkage parameter is derived. The performance of the existing estimators and proposed estimator is evaluated through Monte Carlo simulations and two real data applications. The results clearly reveal that the proposed estimator outperforms the existing estimators in the mean squared error sense.

泊松回归是应用科学中非常常用的计数数据建模技术，其中模型参数通常通过最大似然法估计。然而，多重共线性的存在扩大了最大似然 (ML) 估计器的方差，并且估计的参数给出了不稳定的结果。在本文中，引入了一种新的线性化岭泊松估计器来处理多重共线性问题。基于ML估计器的渐近特性，得到了所提估计器的偏差、协方差和均方误差，并推导出了收缩参数的最优选择。现有估计器和提议的估计器的性能通过蒙特卡罗模拟和两个真实数据应用程序进行评估。