  We focus on the construction of confidence corridors for multivariate
nonparametric generalized quantile regression functions. This construction is
based on asymptotic results for the maximal deviation between a suitable
nonparametric estimator and the true function of interest which follow after a
series of approximation steps including a Bahadur representation, a new strong
approximation theorem and exponential tail inequalities for Gaussian random
fields. As a byproduct we also obtain confidence corridors for the regression
function in the classical mean regression. In order to deal with the problem of
slowly decreasing error in coverage probability of the asymptotic confidence
corridors, which results in meager coverage for small sample sizes, a simple
bootstrap procedure is designed based on the leading term of the Bahadur
representation. The finite sample properties of both procedures are
investigated by means of a simulation study and it is demonstrated that the
bootstrap procedure considerably outperforms the asymptotic bands in terms of
coverage accuracy. Finally, the bootstrap confidence corridors are used to
study the efficacy of the National Supported Work Demonstration, which is a
randomized employment enhancement program launched in the 1970s. This article
has supplementary materials.
