Goodness-of-fit tests for a heavy tailed distribution

We study the Kolmogorov–Smirnov test, Berk–Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations.In the simulations, the score test and the integrated score test show the best performance. Although the Berk–Jones test is more powerful than the Kolmogorov–Smirnov test, this does not hold true for their integrated versions; this differs from results in Einmahl et al. [2003. Empirical likelihood based hypothesis testing. Bernoulli 9(2), 267–290], which shows the difference of Berk–Jones test in testing distributions and tails.