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Quantiles Extrèmes Conditionnels by Lekina-A

Quantiles Extrèmes Conditionnels

by Lekina-A
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Book cover type: Paperback
  • ISBN13: 9786131556289
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 156
  • Original Price: GBP 41.0
  • Language: French
  • Edition: N/A
  • Item Weight: 236 grams
  • BISAC Subject(s): Probability & Statistics / General

L'objectif de ce travail est de proposer de nouveaux estimateurs de quantiles extrèmes dans le cadre conditionnel c'est-à-dire dans la situation où la variable d'intérèt Y, supposée aléatoire et réelle, est mesurée simultanément avec une covariable X. Pour ce faire, nous nous intéressons à l'étude des valeurs extrèmes d'un échantillon d'observations indépendantes dont la loi conditionnelle de Y en un point x de la covariable X est à queue lourde. Selon la nature de la covariable, nous considérons deux situations. Primo, lorsque la covariable est déterministe nous proposons d'estimer les quantiles extrèmes par la méthode dite de la fenètre mobile. Secundo, lorsque la covariable est aléatoire, nous montrons que sous certaines conditions, il est possible d'estimer les quantiles extrèmes conditionnels au moyen d'un estimateur à noyau de la fonction de survie conditionnelle. Ce résultat nous permet d'introduire deux versions de l'estimateur de l'indice de queue conditionnel indispensable lorsque l'on veut extrapoler. Nous établissons la loi asymptotique de ces estimateurs. Par ailleurs, nous proposons aussi un nouvel estimateur non conditionnel des quantiles.

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