In this paper, we study the problem of estimating non-parametrically a
quantile regression curve as it applies to computing reference values
. We propose an automatic procedure that uses a symmetrized nearest-ne
ighbor kernel estimator of conditional distributions. We also discuss
ways of measuring the dispersion of the quantile regression estimator.
One is based on the asymptotic distribution of such quantiles, while
the other relies on the bootstrap method. The results of a small simul
ation study show that the methods of the paper perform rather well eve
n in a situation where a good parametric solution is available. As an
example, we analyze a small part of a data set that was collected to e
stablish reference values for blood velocity in different parts of the
umbilical cord of human fetuse as they grow toward birth.