A Tutorial on Asymptotic Properties for Biostatisticians with Applications to COVID-19 Data
This provides a methodological framework for biostatisticians dealing with real-world data like COVID-19, but it is incremental as it extends existing asymptotic theory to more realistic scenarios.
The paper tackles the problem of deriving asymptotic properties for statistical estimators under non-iid conditions, such as fixed designs, by building a general roadmap and applying it to Poisson regression with COVID-19 data to demonstrate practical utility.
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.