  A novel method for computing exact p-values of one-sided statistics from the
Kolmogorov-Smirnov family is presented. It covers the Higher Criticism
statistic, one-sided weighted Kolmogorov-Smirnov statistics, and the one-sided
Berk-Jones statistics. In addition to p-values, the method can also be used for
power analysis, finding alpha-level thresholds, and the construction of
confidence bands for the empirical distribution function.
  With its quadratic runtime and numerical stability, the method easily scales
to sample sizes in the hundreds of thousands and takes less than a second to
run on a sample size of 25,000. This allows practitioners working on large data
sets to use exact finite-sample computations instead of approximation schemes.
  The method is based on a reduction to the boundary-crossing probability of a
pure jump stochastic process. FFT convolutions of two different sizes are then
used to efficiently propagate the probabilities of the non-crossing paths. This
approach has applications beyond statistics, for example in financial risk
modeling.
