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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

Author

Listed:
  • 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.

Suggested Citation

  • Jeroen Hinloopen & Rien Wagenvoort, 2010. "Identifying All Distinct Sample P-P Plots, with an Application to the Exact Finite Sample Distribution of the L1-FCvM Test Statistic," Tinbergen Institute Discussion Papers 10-083/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20100083
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    References listed on IDEAS

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    1. Schmid, Friedrich & Trede, Mark, 1995. "A distribution free test for the two sample problem for general alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 409-419, October.
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    Cited by:

    1. Jeroen Hinloopen & Rien J.L.M. Wagenvoort & Charles van Marrewijk, 2012. "A k-sample homogeneity test: the Harmonic Weighted Mass index," International Econometric Review (IER), Econometric Research Association, vol. 4(1), pages 17-39, April.

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    More about this item

    Keywords

    Sample p-p plot; EDF test; finite sample distribution; limiting distribution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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