On the Exact Finite Sample Distribution of the L 1-FCvM Test Statistic |
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Authors: | Jeroen Hinloopen Rien J. L. M. Wagenvoort |
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Affiliation: | 1. Amsterdam School of Economics , University of Amsterdam, and Tinbergen Institute , Amsterdam , The Netherlands;2. European Investment Bank , Boulevard Konrad Adenauer, Luxemburg |
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Abstract: | We derive the exact finite sample distribution of the L1 -version of the Fisz–Cramér–von Mises test statistic (FCvM 1). We first characterize the set of all distinct sample p-p plots for two balanced samples of size n absent ties. Next, we order this set according to the corresponding value of FCvM 1. Finally, we link these values to the probabilities that the underlying p-p plots emerge. Comparing the finite sample distribution with the (known) limiting distribution shows that the latter can always be used for hypothesis testing: although for finite samples the critical percentiles of the limiting distribution differ from the exact values, this will not lead to differences in the rejection of the underlying hypothesis. |
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Keywords: | EDF test Finite sample distribution Limiting distribution Sample p-p plot |
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