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标题：Regenerative block-bootstrap confidence intervals for tail and extremal indexes
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作者：Patrice Bertail ; Stéphan Clémençon ; Jessica Tressou 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：1224-1248
DOI：10.1214/13-EJS807
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Regenerative Markov chain;Nummelin splitting technique;extreme value statistics;cycle submaximum;Hill estimator;ex tremal index;regenerative-block bootstrap.