  Nonparametric regression is a standard statistical tool with increased
importance in the Big Data era. Boundary points pose additional difficulties
but local polynomial regression can be used to alleviate them. Local linear
regression, for example, is easy to implement and performs quite well both at
interior as well as boundary points. Estimating the conditional distribution
function and/or the quantile function at a given regressor point is immediate
via standard kernel methods but problems ensue if local linear methods are to
be used. In particular, the distribution function estimator is not guaranteed
to be monotone increasing, and the quantile curves can "cross". In the paper at
hand, a simple method of correcting the local linear distribution estimator for
monotonicity is proposed, and its good performance is demonstrated via
simulations and real data examples.
