Estimation of the incubation time distribution for COVID-19

TL;DR

This paper develops a smooth nonparametric method to estimate the incubation period distribution of COVID-19, offering advantages over parametric models and providing computational tools for implementation.

Contribution

It introduces a smooth nonparametric estimation approach for COVID-19 incubation times and compares it to parametric methods, with theoretical convergence rates and practical R scripts.

Findings

Smooth estimator converges at rate n^{2/7}

Nonparametric MLE computed via iterative convex minorant

Computational tools provided as R scripts

Abstract

We consider smooth nonparametric estimation of the incubation time distribution of COVID-19, in connection with the investigation of researchers from the National Institute for Public Health and the Environment (Dutch: RIVM) of 88 travelers from Wuhan: Backer et al (2020). The advantages of the smooth nonparametric approach w.r.t. the parametric approach, using three parametric distributions (Weibull, log-normal and gamma) in Backer et al (2020) is discussed. It is shown that the typical rate of convergence of the smooth estimate of the density is $n^{2/7}$ in a continuous version of the model, where $n$ is the sample size. The (non-smoothed) nonparametric maximum likelihood estimator (MLE) itself is computed by the iterative convex minorant algorithm (Groeneboom and Jongbloed (2014)). All computations are available as {\tt R} scripts in Groeneboom (2020).