Tail dimension reduction for extreme quantile estimation
type: Item
instance of: scholarly article
title: Tail dimension reduction for extreme quantile estimation
zbMATH Open document ID: 1396.62097
author: Laurent Gardes
published in: Extremes
publication date: 2018-04-16T00:00:00Z
review text: Given covariates \((Y,X) \in \mathbb{R} \times \mathbb{R}^p\), a problem of quantile estimation \(Q(\alpha|X)=\inf\{y:\mathbb{P}(Y>y|X)\leq \alpha\}\) is considered under the assumption \(\alpha \to 0\), i.e., the problem of quantile estimation for the tail of the conditional distribution. In this case, the support of \(X\) may be only sparsely populated by data points if the dimension \(p\) is large. In the article, it is proposed to reduce the dimension by the replacement of \(X\) by \(B^TX\), where \(B\) is a \((p\times q)\)-matrix and \(q < p\). Conditions for the equivalence of \(Q(\alpha|X)\) and \(Q(\alpha|B^TX)\), the determination of an appropriate matrix \(B\) and a quantile estimator are presented. The results are illustrated on simulated data and on a real dataset.
reviewed by: Alex V. Kolnogorov
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 6860552
zbMATH Keywords: regression
zbMATH Keywords: extreme quantile
zbMATH Keywords: dimension reduction
zbMATH Keywords: kernel smoothing
MaRDI profile type: Publication
full work available at URL: s10687-017-0300-x
OpenAlex ID: W2409075483
cites work: Q5429809
cites work: Q3690843
cites work: Nonparametric estimates of regression quantiles and their local Bahadur representation
cites work: On the Interpretation of Regression Plots
cites work: Likelihood-Based Sufficient Dimension Reduction
cites work: Comment
cites work: On kernel smoothing for extremal quantile regression
cites work: Kernel estimators of extreme level curves
cites work: Q3486670
cites work: Local Likelihood Smoothing of Sample Extremes
cites work: Q5485944
cites work: Q3540680
cites work: Sliced inverse regression in reference curves estimation
cites work: A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes
cites work: Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels
cites work: Functional kernel estimators of large conditional quantiles
cites work: On the estimation of the functional Weibull tail-coefficient
cites work: Q3339943
cites work: Sur la distribution limite du terme maximum d'une série aléatoire
cites work: `` Direct Search'' Solution of Numerical and Statistical Problems
cites work: Semiparametric least squares (SLS) and weighted SLS estimation of single-index models
cites work: Regression Quantiles
cites work: Sliced Inverse Regression for Dimension Reduction
cites work: On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma
cites work: Q5509408
cites work: On Estimation of a Probability Density Function and Mode
cites work: Data mining to investigate the meteorological drivers for extreme ground level ozone events
cites work: Model-based SIR for dimension reduction
cites work: Tail Index Regression
cites work: Single-index quantile regression
cites work: Model checking in regression via dimension reduction
cites work: Local Linear Quantile Regression
DOI: 10.1007/S10687-017-0300-X
Recommended article: Q5303070
Recommended article: Extreme quantile regression in a proportional tail framework
Recommended article: Extreme Quantile Estimation Based on the Tail Single-index Model
Recommended article: Estimation of extreme quantiles from heavy and light tailed distributions
Recommended article: Tail estimates motivated by extreme value theory
Recommended article: Improved reduced-bias tail index and quantile estimators
Recommended article: A new extreme quantile estimator for heavy-tailed distributions
Recommended article: Bias reduction and explicit semi-parametric estimation of the tail index
Recommended article: Extremal quantile regression
description: scientific article; zbMATH DE number 6860552