  Weighted log-rank tests are arguably the most widely used tests by
practitioners for the two-sample problem in the context of right-censored data.
Many approaches have been considered to make weighted log-rank tests more
robust against a broader family of alternatives, among them, considering linear
combinations of weighted log-rank tests, and taking the maximum among a finite
collection of them. In this paper, we propose as test statistic the supremum of
a collection of (potentially infinite) weight-indexed log-rank tests where the
index space is the unit ball in a reproducing kernel Hilbert space (RKHS). By
using some desirable properties of RKHSs we provide an exact and simple
evaluation of the test statistic and establish connections with previous tests
in the literature. Additionally, we show that for a special family of RKHSs,
the proposed test is omnibus. We finalise by performing an empirical evaluation
of the proposed methodology and show an application to a real data scenario.
Our theoretical results are proved using techniques for double integrals with
respect to martingales that may be of independent interest.
