A kernel estimator (KQ) of the quantile function is presented here. Bo
undary kernels are used for extrapolation of tail quantiles. The bandw
idth of the estimator is chosen using an automatic, ''plug-in'' method
. Confidence intervals for the estimated quantile are estimated by boo
tstrapping. Comparisons of the estimator with selected tail probabilit
y estimators are offered. The KQ estimator presented here is shown to
be competitive with other estimators.