Nonparametric comparison of quantile curves

Abstract

A new test for comparing conditional quantile curves is proposed which is able to detect Pitman alternatives converging to the null hypothesis at the optimal rate. The basic idea of the test is to measure differences between the curves by a process of integrated non parametric estimates of the quantile curve. We prove weak convergence of this process to a Gaussian process and study the finite sample properties of a Kolmogorov-Smirnov test by means of a simulation study.