  Survival Analysis and Reliability Theory are concerned with the analysis of
time-to-event data, in which observations correspond to waiting times until an
event of interest such as death from a particular disease or failure of a
component in a mechanical system. This type of data is unique due to the
presence of censoring, a type of missing data that occurs when we do not
observe the actual time of the event of interest but, instead, we have access
to an approximation for it given by random interval in which the observation is
known to belong. Most traditional methods are not designed to deal with
censoring, and thus we need to adapt them to censored time-to-event data. In
this paper, we focus on non-parametric goodness-of-fit testing procedures based
on combining the Stein's method and kernelized discrepancies. While for
uncensored data, there is a natural way of implementing a kernelized Stein
discrepancy test, for censored data there are several options, each of them
with different advantages and disadvantages. In this paper, we propose a
collection of kernelized Stein discrepancy tests for time-to-event data, and we
study each of them theoretically and empirically; our experimental results show
that our proposed methods perform better than existing tests, including
previous tests based on a kernelized maximum mean discrepancy.
