Nonparametric estimation of the incubation time distribution

TL;DR

This paper explores nonparametric estimation of disease incubation times, showing that smoothing techniques lead to normal limit distributions and more reliable inference compared to traditional parametric methods.

Contribution

It demonstrates the advantages of smoothing in nonparametric MLEs for incubation time models, improving inference accuracy over parametric approaches.

Findings

Smoothed estimators have normal limit distributions.

Parametric models like Weibull can be inconsistent.

Bootstrap methods are proposed for confidence intervals.

Abstract

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. The classical bootstrap, based on the nonparametric MLE itself, has been proved to be inconsistent in this situation.