On Optimising the Estimation of Extreme Value Quantiles of a Probability Distribution

In this paper, a new extreme value quantile estimator is given and its limit properties are discussed. Under the asymptotic second moment principle, recurring to sub-sample bootstrap method, the optimality problem of sample fraction in extreme value quantile estimation is solved, and the limit properties are proved. We prove our sample fraction is optimal under the asymptotic second moment principle, also an adaptive bootstrap procedure is given.