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 ()
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Lucia Alessi: European Central Bank, Frankfurt, Germany; Laboratory of Economics and Management, Sant'Anna School of Advanced Studies, Pisa, Italy

Advances in Complex Systems (ACS), 2009, vol. 12, issue 02, pages 157-167

Abstract: 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. Furthermore, we present some simple examples 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; Cramér–Von Mises statistic; empirical distribution function; Monte-Carlo simulations; 02.50.Ng; 02.70.Uu; 05.10.Ln (search for similar items in EconPapers)
Date: 2009

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Working Paper: On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters (2007)
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