On the Exact Finite Sample Distribution of the L1 -FCvM Test Statistic
AbstractWe derive the exact finite sample distribution of the L 1-version ofthe Fisz-Cramér-von Mises test statistic ( L1 -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.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-083/1.
Date of creation: 19 May 2011
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Sample p-p plot; EDF test; finite sample distribution; limiting distribution;
Find related papers by 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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