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On the exact finite sample distribution of the L1-FCvM test statistic
Communications in Statistics - Simulation and Computation (2014)
  • Jeroen Hinloopen
  • Rien Wagenvoort
Abstract

We derive the exact finite sample distribution of the L1-version of the Fisz-Cramér-von Mises test statistic (L1-FCvM). We first characterize the set of all distinct sample p-p plots for two balanced sampleof size n absent ties. Next, we order this set according to the corresponding value of L1-FCvM. 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.

Keywords
  • Sample p-p plot,
  • EDF test,
  • finite sample distribution,
  • limiting distribution
Disciplines
Publication Date
2014
Citation Information
Jeroen Hinloopen and Rien Wagenvoort. "On the exact finite sample distribution of the L1-FCvM test statistic" Communications in Statistics - Simulation and Computation Vol. 43 Iss. 6 (2014)
Available at: http://works.bepress.com/hinloopen/9/