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.