Reiss and Thomas' automatic selection of the number of extremes

DOI10.1016/j.csda.2003.11.011zbMath1430.62096OpenAlexW1967070567MaRDI QIDQ957044

Cláudia Neves, M. Isabel Fraga Alves

Publication date: 26 November 2008

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.csda.2003.11.011

zbMATH Keywords

simulationmean squared errorregular variationsemiparametric estimationgeneralized extreme value distributiongeneralized Pareto distribution

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Statistics of extreme values; tail inference (62G32)

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Cites Work

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• Tail estimates motivated by extreme value theory
• On the estimation of the extreme-value index and large quantile estimation
• A moment estimator for the index of an extreme-value distribution
• Regression with response distributions of Pareto-type
• On asymptotic normality of Hill's estimator for the exponent of regular variation
• Laws of large numbers for sums of extreme values
• Approximate distributions of order statistics. With applications to nonparametric statistics
• Statistical inference using extreme order statistics
• A simple general approach to inference about the tail of a distribution
• Smoothing the moment estimator of the extreme value parameter
• Optimal choice of sample fraction in extreme-value estimation
• The bootstrap methodology in statistics of extremes -- choice of optimal sample fraction
• Tail index estimation and an exponential regression model
• Selecting the optimal sample fraction in univariate extreme value estimation
• How to make a Hill plot.
• A location invariant Hill-type estimator
• SLOW VARIATION WITH REMAINDER: THEORY AND APPLICATIONS
• Comparison of tail index estimators
• Smoothing the Hill Estimator
• Using a bootstrap method to choose the sample fraction in tail index estimation
• A bootstrap-based method to achieve optimality in estimating the extreme-value index