Limit theorems for empirical processes of cluster functionals
From MaRDI portal
Publication:988001
DOI10.1214/09-AOS788zbMath1210.62051arXiv0910.0343MaRDI QIDQ988001
Publication date: 24 August 2010
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0910.0343
rare eventsblock bootstrapextremesuniform central limit theoremabsolute regularityclustering of extremeslocal empirical processestail distribution function
Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Functional limit theorems; invariance principles (60F17)
Related Items
Discussion of ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’ ⋮ The tail process and tail measure of continuous time regularly varying stochastic processes ⋮ Correction to: ``Limit theorems for empirical processes of cluster functionals ⋮ Statistical analysis for stationary time series at extreme levels: new estimators for the limiting cluster size distribution ⋮ Inference on the tail process with application to financial time series modeling ⋮ A large deviations approach to limit theory for heavy-tailed time series ⋮ Estimation of cluster functionals for regularly varying time series: runs estimators ⋮ Multiple block sizes and overlapping blocks for multivariate time series extremes ⋮ Dependent Lindeberg central limit theorem for the fidis of empirical processes of cluster functionals ⋮ Extreme Value Theory and Statistics of Univariate Extremes: A Review ⋮ Weighted weak convergence of the sequential tail empirical process for heteroscedastic time series with an application to extreme value index estimation ⋮ Large deviations of \(\ell^p\)-blocks of regularly varying time series and applications to cluster inference ⋮ Extreme value inference for heterogeneous power law data ⋮ Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds ⋮ Statistics for heteroscedastic time series extremes ⋮ Asymptotic properties of the tail distribution and Hill's estimator for shot noise sequence ⋮ Extreme M-quantiles as risk measures: from \(L^{1}\) to \(L^{p}\) optimization ⋮ Estimation of the tail index for lattice-valued sequences ⋮ Statistics for tail processes of Markov chains ⋮ Cluster based inference for extremes of time series ⋮ Asymptotic normality of the likelihood moment estimators for a stationary linear process with heavy-tailed innovations ⋮ Editorial: Special issue on time series extremes ⋮ On the measurement and treatment of extremes in time series ⋮ The tail empirical process of regularly varying functions of geometrically ergodic Markov chains ⋮ Weak convergence of a pseudo maximum likelihood estimator for the extremal index ⋮ Ordinal patterns in clusters of subsequent extremes of regularly varying time series ⋮ Tail risk inference via expectiles in heavy-tailed time series ⋮ Asymptotics for sliding blocks estimators of rare events ⋮ Bootstrapping Hill estimator and tail array sums for regularly varying time series ⋮ Estimation of cluster functionals for regularly varying time series: sliding blocks estimators ⋮ Statistical inference for heavy tailed series with extremal independence ⋮ Trend detection for heteroscedastic extremes ⋮ A horse race between the block maxima method and the peak-over-threshold approach ⋮ Extremes of stationary random fields on a lattice
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Extreme quantile estimation for dependent data, with applications to finance
- Two likelihood-based semiparametric estimation methods for panel count data with covariates
- Weak convergence of the tail empirical process for dependent sequences
- Weak convergence of partial sums of absolutely regular sequences
- Conditions for sample-continuity and the central limit theorem
- Poisson and Gaussian approximation of weighted local empirical processes
- On the distribution of tail array sums for strongly mixing stationary sequences
- The \(L_1\)-norm density estimator process
- Two estimators of the mean of a counting process with panel count data.
- Weighted approximations of tail processes for \(\beta\)-mixing random variables.
- On high level exceedance modeling and tail inference
- Weak convergence and empirical processes. With applications to statistics
- Modelling dependence uncertainty in the extremes of Markov chain
- Uniform in Bandwidth Estimation of Integral Functionals of the Density Function
- Uniform Central Limit Theorems
- Models for the extremes of Markov chains
- Functionals of clusters of extremes
- The distributions of cluster functionals of extreme events in a dth-order Markov chain
- Extreme value theory for stochastic processes
- On uniform convergence of measures
