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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

Author

Listed:
  • 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.

Suggested Citation

  • Marco Capasso & Lucia Alessi & Matteo Barigozzi & Giorgio Fagiolo, 2007. "On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters," LEM Papers Series 2007/23, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2007/23
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    Cited by:

    1. Matthias Duschl & Thomas Brenner, 2013. "Characteristics of regional industry-specific employment growth rates' distributions," Papers in Regional Science, Wiley Blackwell, vol. 92(2), pages 249-270, June.
    2. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    3. Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2010. "On the distributional properties of household consumption expenditures: the case of Italy," Empirical Economics, Springer, vol. 38(3), pages 717-741, June.
    4. Lunardi, José T. & Miccichè, Salvatore & Lillo, Fabrizio & Mantegna, Rosario N. & Gallegati, Mauro, 2014. "Do firms share the same functional form of their growth rate distribution? A statistical test," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 140-164.
    5. Iván Blanco, Juan Ignacio Peña, and Rosa Rodriguez, 2018. "Modelling Electricity Swaps with Stochastic Forward Premium Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

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