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| HAL: hal-00214305, version 2 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2008-01-24) | v2 (2008-03-27) |
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| A regeneration-based runs estimator for the extremal index in the Markov setup |
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| Patrice Bertail 1Stephan Clemencon 2 |
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| (2008-01-24) |
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| It is the purpose of this paper to introduce a novel estimator for the extremal index of an instantaneous function {f(Xn)}n of a regenerative Harris Markov chain X, based on the renewal properties of the latter. The estimate proposed may be viewed as a "regenerative version" of the runs estimator, insofar as it measures the clustering tendency of high threshold exceedances within regeneration cycles. Strong consistency of this estimator is established under mild stochastic stability assumptions and a simulation result is displayed in the case when the underlying chain is the waiting process related to a simple M/M/1 queue. |
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| 1: | Modélisation aléatoire de Paris X (MODAL'X) |
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Université Paris X - Paris Ouest Nanterre La Défense |
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| 2: | Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) |
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Télécom ParisTech – CNRS : UMR5141 |
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| 3: | Méthodologies d'Analyse de Risque Alimentaire (MET@RISK) |
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Institut national de la recherche agronomique (INRA) : UR1204 |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Regenerative Markov Chain – Extremal Index – Runs Estimator |
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| Attached file list to this document: | |||||
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| hal-00214305, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00214305 | |
| oai:hal.archives-ouvertes.fr:hal-00214305 | |
| From: Jessica Tressou | |
| Submitted on: Thursday, 27 March 2008 12:25:23 | |
| Updated on: Thursday, 27 March 2008 13:41:12 | |
