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

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Author Info

  • Jeroen Hinloopen

    (University of Amsterdam)

  • Rien Wagenvoort

    (European Investment Bank, Luxemburg)

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-083/1.

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Date of creation: 30 Aug 2010
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Handle: RePEc:dgr:uvatin:20100083

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Web page: http://www.tinbergen.nl

Related research

Keywords: Sample p-p plot; EDF test; finite sample distribution; limiting distribution;

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