Nonparametric estimation of the incubation time distribution

TL;DR

This paper explores nonparametric methods for estimating disease incubation time distributions, demonstrating their advantages over traditional parametric models through theoretical analysis and practical density estimation.

Contribution

It introduces nonparametric maximum likelihood estimators for incubation times, analyzing their convergence and limit behavior, and compares them with classical parametric approaches.

Findings

Nonparametric MLE converges at a cube root rate.

Limit distribution of the MLE is Chernoff's distribution.

Density estimates reveal finer details of the incubation time distribution.

Abstract

We discuss nonparametric estimators of the distribution of the incubation time of a disease. The classical approach in these models is to use parametric families like Weibull, log-normal or gamma in the estimation procedure. We analyze instead the nonparametric maximum likelihood estimator (MLE) and show that, under some conditions, its rate of convergence is cube root $n$ and that its limit behavior is given by Chernoff's distribution. We also study smooth estimates, based on the MLE. The density estimates, based on the MLE, are capable of catching finer or unexpected aspects of the density, in contrast with the classical parametric methods. {\tt R} scripts are provided for the nonparametric methods.