We discuss quantile estimation, for probability distribution functions,
both in the center of the distribution, and in the tails.
In the center of the distribution, we consider L-estimators, that is, linear
combinations of order statistics. In particular, we discuss im- provements
of the Harrell-Davis estimator, as well as optimal L-estima- tors constructed
by bootstrap methodolgy.
For the tail of the distribution, we use a cross validation scheme to find
estimators of extreme quantiles. To reduce the bias, due to low speed of
convergence, we use second order theory of regular variation.
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