Optimal Choice of Sample Fraction in Extreme-Value Estimation

A. L. M. Dekkers and L. Dehaan

Journal of Multivariate Analysis, 1993, vol. 47, issue 2, 173-195

Abstract: We study the asymptotic bias of the moment estimator [gamma]n for the extreme-value index [gamma] [set membership, variant] 5 under quite natural and general conditions on the underlying distribution function. Furthermore the optimal choice for the sample franction in estimating [gamma] is considered by minimizing the mean squared error of [gamma]n - [gamma]. The results cover all three limiting types of extreme-value theory. The connection between statistics and regular variation and [Pi]-variation is handled in a systematic way.

Date: 1993
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