Identifying All Distinct Sample P-P Plots, with an Application to the Exact Finite Sample Distribution of the L1-FCvM Test Statistic

Jeroen Hinloopen and Rien Wagenvoort
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Jeroen Hinloopen: University of Amsterdam
Rien Wagenvoort: European Investment Bank, Luxemburg

No 10-083/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: P-p plots contain all the information that is needed for scale-invariant comparisons. Indeed, Empirical Distribution Function (EDF) tests translate sample p-p plots into a single number. In this paper we characterize the set of all distinct p-p plots for two balanced sample of size n absent ties. Distributions of EDF test statistics are embedded in this set. It is thus used to derive the exact finite sample distribution of the L 1 -version of the Fisz-Cramér-von Mises test. Comparing this 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.

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: 2010-08-30
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Citations: View citations in EconPapers (1)

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