Right Tail Points Unbiased Estimate

Consider a distribution function F, which is in the maximum domain of attraction of an extreme value distribution. When its extreme value indexγ<0, the right end-point of the distribution is finite. Recently Li and Peng (2009) proposed a bias reduction method for estimating the endpoint of a distribution function via an external estimator for the so-called second order parameter. Unlike the same study for the tail index of a heavy tailed distribution, the above procedure requires a certain rate of convergence of the external estimator rather than consistence. This makes the choice of such an external estimator impractical. In this paper, we propose a new bias reduction method which estimates all parameters by using the same number of upper order statistics.