- Identifying all distinct sample p-p plots, with an application to the exact finite sample distribution of the L1-FCvM test statistic
- Number of pages
- Amsterdam [etc.]: Tinbergen Institute
- Tinbergen Institute discussion paper
- Volume | Edition (Serie)
- TI 2010-083/1
- Document type
- Working paper
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
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 L1-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.
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