  In this paper we consider the estimation problem for high quantiles of a
heavy-tailed distribution from block data when only a few largest values are
observed within blocks. We propose estimators for high quantiles and prove that
these estimators are asymptotically normal. Furthermore, we employ empirical
likelihood method and adjusted empirical likelihood method to constructing the
confidence intervals of high quantiles. Through a simulation study we also
compare the performance of the normal approximation method and the adjusted
empirical likelihood methods in terms of the coverage probability and length of
the confidence intervals.
