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Regenerative block-bootstrap confidence intervals for tail and extremal indexes

Authors
  • Bertail, Patrice
  • Clemencon, Stephan
  • Tressou-Cosmao, Jessica
Publication Date
2013
Source
HAL-Paris 13
Keywords
License
Unknown
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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 is an element of 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, there generative 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.

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