  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.
