  Various indicators and measures of the real life procedures rise up as
functionals of the quantile process of a parent random variable Z. However, Z
can be observed only through a response in a linear model whose covariates are
not under our control and the probability distribution of error terms is
generally unknown. The problem is that of nonparametric estimation or other
inference for such functionals. We propose an estimation procedure based on the
averaged two-step regression quantile, recently developed by the authors,
combined with an R-estimator of slopes of the linear model.
