Goodness-of-fit tests for a heavy tailed distribution

Abstract

For testing whether a distribution function is heavy tailed, we study theKolmogorov test, Berk-Jones test, score test and their integratedversions. A comparison is conducted via Bahadur efficiency and simulations.The score test and the integrated score test show the best performance.Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnovtest, this does not hold true for their integrated versions; this differsfrom results in \\citet{EinmahlMckeague2003}, which shows the difference ofBerk-Jones test in testing distributions and tails.Bahadur efficiency;heavy tail;tail index