We generalize the na\"ive estimator of a Poisson regression model with measurement errors as discussed in Kukush et al. [1]. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the explanatory variable and measurement error are not limited to a normal distribution. We clarify the requirements for the existence of the na\"ive estimator and derive its asymptotic bias and asymptotic mean squared error (MSE). In addition, we propose a consistent estimator of the true parameter by correcting the bias of the na\"ive estimator. As illustrative examples, we present simulation studies that compare the performance of the na\"ive estimator and new estimator for a Gamma explanatory variable with a normal error or a Gamma error.

翻译：我们用Kukush等人([1])所讨论的测量误差来概括Poisson回归模型的na”估计值。解释变量并不总是按其假设的通常分布。在本研究中,我们假设解释变量和测量误差不局限于正常分布。我们澄清了对na\'ive估计值存在的要求,并得出其无症状偏差和无症状平均正方差(MSE)。此外,我们提出一个一致的正确参数估计值,纠正na\'ive估计值的偏差。作为示例,我们提出模拟研究,将一个伽玛解释变量的天体测量值和新的估计值与正常错误或伽玛误差进行比较。