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On the Exact Finite Sample Distribution of the L1 -FCvM Test Statistic

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  • Jeroen Hinloopen

    (University of Amsterdam)

Abstract

We derive the exact finite sample distribution of the L 1 -version ofthe Fisz-Cramér-von Mises test statistic ( L 1 -FCvM). We first characterizethe set of all distinct sample p-p plots for two balanced sampleof size n absent ties. Next, we order this set according to the correspondingvalue of L 1 -FCvM. Finally, we link these values to theprobabilities that the underlying p-p plots emerge. Comparing the finitesample distribution with the (known) limiting distribution showsthat the latter can always be used for hypothesis testing: although forfinite samples the critical percentiles of the limiting distribution differfrom the exact values, this will not lead to differences in the rejectionof the underlying hypothesis.

Suggested Citation

  • Jeroen Hinloopen, 2011. "On the Exact Finite Sample Distribution of the L1 -FCvM Test Statistic," Tinbergen Institute Discussion Papers 11-083/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110083
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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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    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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