Estimation of extreme conditional quantiles under a general tail-first-order condition
type: Item
instance of: scholarly article
title: Estimation of extreme conditional quantiles under a general tail-first-order condition
zbMATH Open document ID: 1446.62118
author: Laurent Gardes
author: Armelle Guillou
author: Claire Roman
published in: Annals of the Institute of Statistical Mathematics
publication date: 2020-07-20T00:00:00Z
review text: The authors consider the problem of the estimation of an extreme conditional quantile. Let \(Y\) be a real-valued random variable and \(X\) be an explanatory random vector of dimension \(p \in \mathbb{N} \setminus \left\lbrace 0 \right\rbrace \). The conditional quantile of level \(\alpha \in [0,1]\) of \(Y\) given \(\left\lbrace X=x_{0}\right\rbrace \) is \(Q\left(\alpha\mid x_{0} \right) := \inf \left\lbrace y \in \mathbb{R}; \, S\left(y\mid x_{0} \right) \le \alpha \right\rbrace \), where \(S\left( \cdot\mid x_{0} \right) := \mathbb{P} \left(Y>\cdot\mid X=x_{0} \right) \) is the conditional survival function. Given \(n\) independent copies \(\left(X_{1},Y_{1}\right),\dots,\left(X_{n},Y_{n}\right) \) of \(\left(X,Y\right) \), they focus on the so-called indirect estimation method: starting from a suitable estimator \(\hat{S}_{n}\left(\cdot\mid x_{0} \right)\) of \(S\left(\cdot\mid x_{0} \right)\), the associated estimator of \(Q\left(\alpha\mid x_{0} \right)\) is given by \(\hat{Q}_{n}\left(\alpha\mid x_{0} \right) := \inf \left\lbrace y \in \mathbb{R}; \, \hat{S}_{n}\left(y\mid x_{0} \right) \le \alpha \right\rbrace\).
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62P35
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 7223266
zbMATH Keywords: extreme quantile
zbMATH Keywords: local estimation
zbMATH Keywords: asymptotic normality
zbMATH Keywords: earthquake magnitude
MaRDI profile type: Publication
full work available at URL: s10463-019-00713-7
OpenAlex ID: W2905648946
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Wikidata QID: Q128061434
DOI: 10.1007/S10463-019-00713-7
description: scientific article; zbMATH DE number 7223266