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...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 47; no. 2; pp. 173 - 195
Main Authors Dekkers, A.L.M., Dehaan, L.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.11.1993
Elsevier
SeriesJournal of Multivariate Analysis
Subjects
Distribution theory
Exact sciences and technology
Mathematics
Probability and statistics
Sciences and techniques of general use
Statistics
Order statistic
Regular variation
Asymptotic normality
Extreme value
Moment method
Mean square error
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1993.1078