论文标题
带测量误差的泊松回归模型的天真估计器
The naïve estimator of a Poisson regression model with measurement errors
论文作者
论文摘要
如Kukush等人所讨论的那样，我们概括了具有测量误差的泊松回归模型的幼稚估计器。 [1]。解释变量并不总是正态分布。在这项研究中，我们假设解释变量和测量误差不限于正态分布。我们阐明了对幼稚估计量的存在的要求，并得出其渐近偏置和渐近平方误差（MSE）的要求。此外，我们通过纠正幼稚估计器的偏置来提出对真实参数的一致估计器。作为说明性的示例，我们提出了模拟研究，以比较纯净的估计量和新的估计量的性能，以伽马解释变量具有正常误差或伽玛误差。
We generalize the naïve 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 naïve 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 naïve estimator. As illustrative examples, we present simulation studies that compare the performance of the naïve estimator and new estimator for a Gamma explanatory variable with a normal error or a Gamma error.
