Reference values obtained by kernel-based estimation of quantile regressions

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-neighbor kernel estimator of conditional distributions. We also discuss ways of measuring the dispersion of 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 simulation study show that the methods of the paper perform rather well even 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 establish reference values for blood velocity in different parts of the umbilical cord of human fetuse as they grow toward birth.