RT Monograph
SR 00
A1 Daouia, Abdelaati
A1 Stupfler, Gilles Claude
A1 Usseglio-Carleve, Antoine
T1 Inference for extremal regression with dependent heavy-tailed data
YR 2022
FD 2022-03
VO 22-1324
SP 31
K1 Conditional quantiles
K1 Conditional expectiles, Extreme value analysis
K1 Heavy tailes
K1 Inference
K1 Mixing
K1 Nonparametric regression
AB Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. Expectiles are themselves quan- tiles of a transformation of the underlying distribution. We develop a fully operational kernel-based inferential theory for extreme conditional quantiles and expectiles in the challenging framework of ↵-mixing, conditional heavy-tailed data whose tail index may vary with covariate values.  This extreme value problem requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling diffi  culties inher- ent to mixing,  smoothing,  and sparsity associated to covariate localization.  We prove the pointwise asymptotic normality of our estimators and obtain optimal rates of convergence reminiscent of those found in the i.i.d. regression setting, but which had not been estab- lished in the conditional extreme value literature so far. Our mathematical assumptions are satisfied in location-scale models with possible temporal misspecification, nonlinear regression models, and autoregressive models, among others. We propose full bias and variance reduction procedures, and simple but e↵ective data-based rules for selecting tun- ing hyperparameters. Our inference strategy is shown to perform well in finite samples and is showcased in applications to stock returns and tornado loss data.
T2 TSE Working Paper
PB TSE Working Paper
PP Toulouse
AV Published
LK https://publications.ut-capitole.fr/id/eprint/45033/
UL http://tse-fr.eu/pub/126785