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

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  • Marco Capasso
  • Lucia Alessi
  • Matteo Barigozzi
  • Giorgio Fagiolo

Abstract

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.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2007/23.

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Date of creation: 06 Nov 2007
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Handle: RePEc:ssa:lemwps:2007/23

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Related research

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;

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Cited by:
  1. Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2007. "On the distributional properties of household consumption expenditures. The case of Italy," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2007/24, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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