  To control the current outbreak of the Coronavirus Disease 2019, constant
monitoring of the epidemic is required since, as of today, no vaccines or
antiviral drugs against it are known. We provide daily updated estimates of the
reproduction number over time at
https://stochastik-tu-ilmenau.github.io/COVID-19/. In this document, we
describe the estimator we are using which was developed in (Fraser 2007),
derive its asymptotic properties, and we give details on its implementation.
Furthermore, we validate the estimator on simulated data, demonstrate that
estimates on real data lead to plausible results, and perform a sensitivity
analysis. Finally, we discuss why the estimates obtained need to be interpreted
with care.
