Regenerative block-bootstrap confidence intervals for tail and extremal indexes

DOI10.1214/13-EJS807zbMath1329.60146MaRDI QIDQ1951155

Patrice Bertail, Jessica Tressou, Stéphan Clémençon

Publication date: 29 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1366896904

zbMATH Keywords

confidence intervalsHill estimatorNummelin splitting techniqueextreme value statisticsregenerative Markov chaincycle submaximumextremal indexesregenerative-block bootstrap procedure

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Markov renewal processes, semi-Markov processes (60K15)

Related Items (2)

On regenerative estimation of extremal index in queueing systems ⋮ Bootstrapping Robust Statistics for Markovian Data Applications to Regenerative R‐Statistics and L‐Statistics

Uses Software

• ismev

Cites Work

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• Extreme values statistics for Markov chains via the (pseudo-) regenerative method
• Markov chains and stochastic stability
• Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems
• Regenerative block-bootstrap for Markov chains
• Inference for the limiting cluster size distribution of extreme values
• Approximate regenerative-block bootstrap for Markov chains
• Tail index estimation for dependent data
• Extreme value theory for queues via cycle maxima
• On blocks and runs estimators of the extremal index
• A tail bootstrap procedure for estimating the tail Pareto-index
• Extremal index estimation for a weakly dependent stationary sequence
• Tail index estimation and an exponential regression model
• New estimators for the extremal index and other cluster characteristics
• A sliding blocks estimator for the extremal index
• Estimating a tail exponent by modelling departure from a Pareto distribution
• Extremal indices, geometric ergodicity of Markov chains and MCMC
• Regeneration-based statistics for Harris recurrent Markov chains
• SLOW VARIATION WITH REMAINDER: THEORY AND APPLICATIONS
• Mixing properties of harris chains and autoregressive processes
• Maxima and exceedances of stationary Markov chains
• A splitting technique for Harris recurrent Markov chains
• Comparison of tail index estimators
• Inference for Clusters of Extreme Values
• Applied Probability and Queues
• Extremes and local dependence in stationary sequences
• Contributions to Doeblin's theory of Markov processes
• Using a bootstrap method to choose the sample fraction in tail index estimation
• A comparison of methods for estimating the extremal index
• An introduction to statistical modeling of extreme values

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