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Optimal Choice of Sample Fraction in Extreme-Value Estimation

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
47
Issue
2
Identifiers
DOI: 10.1006/jmva.1993.1078

Abstract

Abstract We study the asymptotic bias of the moment estimator γ̂ n 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 γ̂ n − 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.

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