Semi-parametric estimation of incubation and generation times by means of Laguerre polynomials

Alexander Kreiss and Ingrid Van Keilegom

Journal of Nonparametric Statistics, 2022, vol. 34, issue 3, 570-606

Abstract: In epidemics many interesting quantities, like the reproduction number, depend on the incubation period (time from infection to symptom onset) and/or the generation time (time until a new person is infected from another infected person). Therefore, estimation of the distribution of these two quantities is of distinct interest. However, this is a challenging problem since it is normally not possible to obtain precise observations of these two variables. Instead, in the beginning of a pandemic, it is possible to observe for transmission pairs the time of symptom onset for both people as well as a window for infection of the first person (e.g. because of travel to a risk area). In this paper we suggest a simple semi-parametric sieve-estimation method based on Laguerre-Polynomials for estimation of these distributions. We provide detailed theory for consistency and illustrate the finite sample performance for small datasets via a simulation study.

Date: 2022
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DOI: 10.1080/10485252.2022.2028281

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