A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but some what less involved case of regularly varying tails (Drees and Kaufmann, 1997); Danielsson et al., 1996). The present paper follows the line of proof of the last mentioned paper.