On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters

Details On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters

2008-03-30

arxiv.org/abs/0803.4322v1

Physics

Data Analysis, Statistics and Probability

11 pages, 1 table, 3 figures (4 boxes)

Scientific paper

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.

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