A Tutorial on Asymptotic Properties for Biostatisticians with Applications to COVID-19 Data

TL;DR

This paper provides a comprehensive guide on deriving asymptotic properties of estimators under fixed, non-iid designs, with practical applications including COVID-19 data analysis.

Contribution

It introduces general procedures for asymptotic analysis under fixed designs and demonstrates their application to COVID-19 data using Poisson regression.

Findings

Asymptotic results extend beyond iid assumptions.

Application to COVID-19 data showcases practical utility.

Provides a roadmap for biostatisticians in complex data settings.

Abstract

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.