TWO APPROACHES TO CONSTRUCTING SIMULTANEOUSCONFIDENCE BOUNDS FOR QUANTILES
M. Csörgő P. Révész
Abstract: Given some regularity conditions on the distribution function
of a random sample the sequence of quantile processes
behaves like a sequence of Brownian
bridges where the inverse of , and
if with the order statistics
of the above sample. First, a sequence of consistent direct
estimators is proposed for the quantile-density function The latter then
also enables us to construct simultaneous confidence bounds for an unknown quantile
function The second approach makes frequently misused heuristic steps
like
precise for large , where is the empirical distribution function of the above random
sample, and for is defined by