On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters
Marco Capasso (),
Lucia Alessi (),
Matteo Barigozzi and
Giorgio Fagiolo ()
LEM Papers Series from Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy
This note 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.
Keywords: Goodness of fit tests; Critical values; Anderson-Darling statistic; Kolmogorov-Smirnov statistic; Kuiper Statistic; Cramer-Von Mises statistic; Empirical Distribution function; Monte-Carlo Simulations (search for similar items in EconPapers)
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Journal Article: ON APPROXIMATING THE DISTRIBUTIONS OF GOODNESS-OF-FIT TEST STATISTICS BASED ON THE EMPIRICAL DISTRIBUTION FUNCTION: THE CASE OF UNKNOWN PARAMETERS (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:ssa:lemwps:2007/23
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