Asymptotic properties of statistical estimators play a significant role both in practice and in theory. However, many asymptotic results in statistics rely heavily on the independent and identically distributed (iid) assumption, which is not realistic when we have fixed designs. In this article, we build a roadmap of general procedures for deriving asymptotic properties under fixed designs and the observations need not to be iid. We further provide their applications in many statistical applications. Finally, we apply our results to Poisson regression using a COVID-19 dataset as an illustration to demonstrate the power of these results in practice.

翻译：统计估计员的无症状特性在实践和理论上都起着重要作用,然而,统计的许多无症状结果严重依赖独立和相同分布的(二d)假设,而当我们有固定的设计时,这种假设是不现实的,在本条中,我们为根据固定的设计产生无症状特性而绘制了一般程序的路线图,观测结果不必是固定的。我们还在许多统计应用中提供了应用。最后,我们用COVID-19数据集来将结果应用于普瓦松回归,作为实例,以展示这些结果在实践中的力量。