On the bootstrap quantile-treatment-effect test

Let {X₁,..., X_n} and {Y₁,..., Y_m} be two samples of independent and identically distributed observations with common continuous cumulative distribution functions F(x) = P(X ≤ x) and G(y) = P(Y ≤ y), respectively. In this article, we would like to test the no quantile treatment effect hypothesis H₀: F = G. We develop a bootstrap quantile-treatment-effect test procedure for testing H₀ under the location-scale shift model. Our test procedure avoids the calculation of the check function (which is non-differentiable at the origin and makes solving the quantile effects difficult in typical quantile regression analysis). The limiting null distribution of the test procedure is derived and the procedure is shown to be consistent against a broad family of alternatives. Simulation studies show that our proposed test procedure attains its type I error rate close to the pre-chosen significance level even for small sample sizes. Our test procedure is illustrated with two real data sets on the lifetimes of guinea pigs from a treatment-control experiment.