On approximating the distributions of goodness-of-fit test statistics   based on the empirical distribution function: The case of unknown parameters
  This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate unknown parameters on each simulated Monte-Carlo sample -- and thus avoiding to employ this information to build the test statistic -- may lead to wrong, overly-conservative testing. Furthermore, we present a simple example suggesting that the impact of this possible mistake may turn out to be dramatic and does not vanish as the sample size increases. 
Marco Capasso, Lucia Alessi, Matteo Barigozzi, Giorgio Fagiolo