  We consider the problem of testing significance of predictors in multivariate
nonparametric quantile regression. A stochastic process is proposed, which is
based on a comparison of the responses with a nonparametric quantile regression
estimate under the null hypothesis. It is demonstrated that under the null
hypothesis this process converges weakly to a centered Gaussian process and the
asymptotic properties of the test under fixed and local alternatives are also
discussed. In particular we show, that - in contrast to the nonparametric
approach based on estimation of $L^2$-distances - the new test is able to
detect local alternatives which converge to the null hypothesis with any rate
$a_n \to 0$ such that $a_n \sqrt{n} \to \infty$ (here $n$ denotes the sample
size). We also present a small simulation study illustrating the finite sample
properties of a bootstrap version of the the corresponding Kolmogorov-Smirnov
test.
