Erik Brodin, Chalmers

On Quantile Estimation

Abstract:

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.