Nonparametric analysis of covariance using quantile curves

Abstract

We consider the problem of testing the equality of J quantile curves from independent samples. A test statistic based on an L^2-distance between non-crossing nonparametric estimates of the quantile curves from the individual samples is proposed. Asymptotic normality of this statistic is established under the null hypothesis, local and fixed alternatives, and the finite sample properties of a bootstrap based version of this test statistic are investigated by means of a simulation study.