Identifying All Distinct Sample P-P Plots, with an Application to the Exact Finite Sample Distribution of the L1-FCvM Test Statistic - Jeroen Hinloopen; Rien Wagenvoort (Tinbergen Institute, 2010)
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 L1-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.
Keywords: C12; C14; C46; 330; Sample p-p plot; EDF test; finite sample distribution; limiting distribution; Statistische Verteilung; Statistischer Test; Nichtparametrisches Verfahren; Theorie