On the Exact Finite Sample Distribution of the L1 -FCvM Test Statistic

Jeroen Hinloopen

No 11-083/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We derive the exact finite sample distribution of the L 1 -version ofthe Fisz-Cramér-von Mises test statistic ( L 1 -FCvM). We first characterizethe set of all distinct sample p-p plots for two balanced sampleof size n absent ties. Next, we order this set according to the correspondingvalue of L 1 -FCvM. Finally, we link these values to theprobabilities that the underlying p-p plots emerge. Comparing the finitesample distribution with the (known) limiting distribution showsthat the latter can always be used for hypothesis testing: although forfinite samples the critical percentiles of the limiting distribution differfrom the exact values, this will not lead to differences in the rejectionof the underlying hypothesis.

Keywords: Sample p-p plot; EDF test; finite sample distribution; limiting distribution (search for similar items in EconPapers)
JEL-codes: C12 C14 C46 (search for similar items in EconPapers)
Date: 2011-05-19
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20110083

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