Optimal Choice of Sample Fraction in Extreme-Value Estimation

We study the asymptotic bias of the moment estimator γ̂n for the extreme-value index γ ∈ R under quite natural and general conditions on the underlying distribution function. Furthermore the optimal choice for the sample franction in estimating γ is considered by minimizing the mean squared error of γ̂n − γ. The results cover all three limiting types of extreme-value theory. The connection between statistics and regular variation and Π-variation is handled in a systematic way.