Open Access
2024 Nonparametric estimation of the incubation time distribution
Piet Groeneboom
Author Affiliations +
Electron. J. Statist. 18(1): 1917-1969 (2024). DOI: 10.1214/24-EJS2243


Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff’s distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the MLE, one gets normal limit distributions and faster rates of convergence. We demonstrate this for a model for the incubation time of a disease. The usual approach in the latter models is to use parametric distributions, like Weibull and gamma distributions, which leads to inconsistent estimators. Smoothed bootstrap methods are discussed for constructing confidence intervals.


I want to thank the referees for their constructive remarks. I also want to thank Geurt Jongbloed for useful discussions.


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Piet Groeneboom. "Nonparametric estimation of the incubation time distribution." Electron. J. Statist. 18 (1) 1917 - 1969, 2024.


Received: 1 November 2022; Published: 2024
First available in Project Euclid: 22 April 2024

Digital Object Identifier: 10.1214/24-EJS2243

Primary: 62G05 , 62N01
Secondary: 62-04

Keywords: Chernoff’s distribution , Covid-19 , incubation time , Kernel estimates , nonparametric MLE , nonparametric SMLE , smoothed bootstrap

Vol.18 • No. 1 • 2024
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