Asymptotic normality of extreme value estimators on \(C[0,1]\)

DOI10.1214/009053605000000831zbMath1091.62041arXivmath/0605612OpenAlexW2950929879MaRDI QIDQ2493560

Tao Lin, John H. J. Einmahl

Publication date: 21 June 2006

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605612

zbMATH Keywords

estimationextreme value indexinfinite-dimensional extremesweak convergence on \(C[0,1\)]

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Functional limit theorems; invariance principles (60F17) Asymptotic properties of parametric tests (62F05)

Related Items (12)

Extreme value estimation for discretely sampled continuous processes ⋮ Approximation and estimation of very small probabilities of multivariate extreme events ⋮ Trends in Extreme Value Indices ⋮ Central limit theorems for local empirical processes near boundaries of sets ⋮ The generalized Pareto process; with a view towards application and simulation ⋮ A CLT for weighted time-dependent uniform empirical processes ⋮ Joint exceedances of the ARCH process ⋮ ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA ⋮ On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation ⋮ Empirical tail copulas for functional data ⋮ Testing for changes in the tail behavior of Brown-Resnick Pareto processes ⋮ A horse race between the block maxima method and the peak-over-threshold approach

Cites Work

• A moment estimator for the index of an extreme-value distribution
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• max-infinitely divisible and max-stable sample continuous processes
• Weak consistency of extreme value estimators in \(C[0,1\)]
• The Edgeworth expansion for distributions of extreme values
• On convergence toward an extreme value distribution in \(C[0,1\)]
• Weak convergence and empirical processes. With applications to statistics
• Estimating the probability of a rare event
• Spatial extremes: models for the stationary case
• On Smooth Statistical Tail Functionals
• Joint exceedances of the ARCH process
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