On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: The case of unknown parameters
AbstractThis 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 InfoPaper 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.
Date of creation: 06 Nov 2007
Date of revision:
Goodness of fit tests; Critical values; Anderson-Darling statistic; Kolmogorov-Smirnov statistic; Kuiper Statistic; Cramer-Von Mises statistic; Empirical Distribution function; Monte-Carlo Simulations;
Other versions of this item:
- Marco Capasso & Lucia Alessi & Matteo Barigozzi & Giorgio Fagiolo, 2009. "On Approximating The Distributions Of Goodness-Of-Fit Test Statistics Based On The Empirical Distribution Function: The Case Of Unknown Parameters," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 157-167.
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- Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2010.
"On the distributional properties of household consumption expenditures: the case of Italy,"
Springer, vol. 38(3), pages 717-741, June.
- Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2007. "On the distributional properties of household consumption expenditures. The case of Italy," LEM Papers Series 2007/24, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
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