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 infection 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.
翻译：在许多令人感兴趣的流行病中,如生殖数,其数量取决于孕育期(从感染到症状发作的时间)和/或生育期(直到新人从另一个感染者感染为止的时间),因此,对这两个数量分布的估计是明显值得注意的,然而,这是一个具有挑战性的问题,因为通常不可能对这两个变量进行精确的观察。相反,在流行病开始的时候,可以观察到感染配对双方的症状发作时间以及第一个人感染的窗口(例如,由于前往一个危险地区)。在本文件中,我们建议根据Laguerre-Polynomicals进行简单的半对准的精细估计方法来估计这些分布。我们通过模拟研究为小型数据集提供了详细的一致性理论,并举例说明了有限的样本性能。
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