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2013 Regenerative block-bootstrap confidence intervals for tail and extremal indexes
Patrice Bertail, Stéphan Clémençon, Jessica Tressou
Electron. J. Statist. 7: 1224-1248 (2013). DOI: 10.1214/13-EJS807

Abstract

A theoretically sound bootstrap procedure is proposed for building accurate confidence intervals of parameters describing the extremal behavior of instantaneous functionals $\{f(X_{n})\}_{n\in\mathbb{N}}$ of a Harris Markov chain $X$, namely the extremal and tail indexes. Regenerative properties of the chain $X$ (or of a Nummelin extension of the latter) are here exploited in order to construct consistent estimators of these parameters, following the approach developed in [10]. Their asymptotic normality is first established and the standardization problem is also tackled. It is then proved that, based on these estimators, the regenerative block-bootstrap and its approximate version, both introduced in [7], yield asymptotically valid confidence intervals. In order to illustrate the performance of the methodology studied in this paper, simulation results are additionally displayed.

Citation

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Patrice Bertail. Stéphan Clémençon. Jessica Tressou. "Regenerative block-bootstrap confidence intervals for tail and extremal indexes." Electron. J. Statist. 7 1224 - 1248, 2013. https://doi.org/10.1214/13-EJS807

Information

Published: 2013
First available in Project Euclid: 25 April 2013

zbMATH: 1329.60146
MathSciNet: MR3056073
Digital Object Identifier: 10.1214/13-EJS807

Subjects:
Primary: 60G70, 60J10, 60K20

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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