A nonparametric test for paired data

Abstract

The paper proposes a weighted Kolmogorov–Smirnov type test for the two-sample problem for paired data. The asymptotic distribution of the test statistic under the null model is derived. The dependence of both the finite sample and the asymptotic distribution of the test statistic on the dependence structure of the data requires the use of the wild bootstrap technique for inference. The related wild bootstrap test turns out to be a consistent asymptotically level α test. With the finite sample correction applied, the test keeps the level well. An extensive simulation study demonstrates good finite sample behaviour of the test in comparison to the existing procedures. The main role in the proofs is played by tools from empirical processes. Additional simulation results, as well as an R code, which allow one to easily repeat the conducted numerical experiments, are attached as Supplementary Material.