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Communications in Statistics - Simulation and Computation

Volume 43, Issue 6, 2014

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On the Exact Finite Sample Distribution of the L 1-FCvM Test Statistic

On the Exact Finite Sample Distribution of the L 1-FCvM Test Statistic

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DOI:
10.1080/03610918.2012.733470
Jeroen Hinloopena & Rien J. L. M. Wagenvoortb

pages 1304-1317

  • Received: 11 Jun 2012
  • Accepted: 19 Sep 2012
  • Accepted author version posted online: 10 Jun 2013
    Published online: 02 Dec 2013
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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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Details

  • Citation information:
  • Received: 11 Jun 2012
  • Accepted: 19 Sep 2012
  • Accepted author version posted online: 10 Jun 2013
  • Published online: 02 Dec 2013

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Author affiliations

  • a Amsterdam School of Economics , University of Amsterdam, and Tinbergen Institute , Amsterdam , The Netherlands
  • b European Investment Bank , Boulevard Konrad Adenauer, Luxemburg

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