Regenerative block-bootstrap confidence intervals for the tail and extremal indexes
Résumé
A theoretically sound bootstrap procedure is proposed for build- ing accurate confidence intervals of parameters describing the extremal be- havior of instantaneous functionals {f(Xn)}n∈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 approx- imate 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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