Residual-based extreme value estimation for heavy tails
Abstract
We consider the estimation of, and inference about, conditional extreme quantiles and related quantities based on non-i.i.d. random variables, termed residuals throughout. This is motivated by the recent use of location-scale regression models to support several extremal regression methods, where the extreme value step is carried out using the residuals of the model, rather than the unobserved i.i.d. errors, following a preliminary model estimation step. We show that residual-based versions of a certain large class of extreme value estimators are asymptotically normal under a high-level condition on the number of residuals considered to be too far from their i.i.d. counterparts. This condition is shown to be substantially weaker than analogous conditions in the recent literature, and we discuss how our theory applies to a wide range of examples containing location-scale parametric regression models, multivariate autoregressive time series, and noisy data models. Finite-sample simulation studies and a real data example illustrate the performance of our estimators and of the asymptotic confidence regions derived from our theoretical results.
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BibTeX
@misc{oesting2026residualbased,
title = {{Residual-based extreme value estimation for heavy tails}},
author = {Marco Oesting and Gilles Stupfler},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-04705855v3},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Residual-based extreme value estimation for heavy tails
AU - Marco Oesting
AU - Gilles Stupfler
PY - 2026
DA - 2026/09/22
PB - HAL
UR - https://hal.science/hal-04705855v3
AB - We consider the estimation of, and inference about, conditional extreme quantiles and related quantities based on non-i.i.d. random variables, termed residuals throughout. This is motivated by the recent use of location-scale regression models to support several extremal regression methods, where the extreme value step is carried out using the residuals of the model, rather than the unobserved i.i.d. errors, following a preliminary model estimation step. We show that residual-based versions of a certain large class of extreme value estimators are asymptotically normal under a high-level condition on the number of residuals considered to be too far from their i.i.d. counterparts. This condition is shown to be substantially weaker than analogous conditions in the recent literature, and we discuss how our theory applies to a wide range of examples containing location-scale parametric regression models, multivariate autoregressive time series, and noisy data models. Finite-sample simulation studies and a real data example illustrate the performance of our estimators and of the asymptotic confidence regions derived from our theoretical results.
ER -