eprintid: 45033 rev_number: 20 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/04/50/33 datestamp: 2022-03-22 09:05:08 lastmod: 2023-08-30 06:58:24 status_changed: 2023-08-30 06:58:24 type: monograph metadata_visibility: show creators_name: Daouia, Abdelaati creators_name: Stupfler, Gilles Claude creators_name: Usseglio-Carleve, Antoine creators_idrefppn: 076657000 creators_idrefppn: 159301602 creators_idrefppn: 23039521X creators_halaffid: 1002422 title: Inference for extremal regression with dependent heavy-tailed data ispublished: pub subjects: subjects_ECO abstract: 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. date: 2022-03 date_type: published publisher: TSE Working Paper official_url: http://tse-fr.eu/pub/126785 faculty: tse divisions: tse keywords: Conditional quantiles keywords: Conditional expectiles, Extreme value analysis keywords: Heavy tailes keywords: Inference keywords: Mixing keywords: Nonparametric regression language: en has_fulltext: TRUE view_date_year: 2022 full_text_status: public monograph_type: working_paper series: TSE Working Paper volume: 22-1324 place_of_pub: Toulouse pages: 31 institution: Université Toulouse 1 Capitole department: Toulouse School of Economics book_title: TSE Working Paper oai_identifier: oai:tse-fr.eu:126785 harvester_local_overwrite: department harvester_local_overwrite: creators_name harvester_local_overwrite: pending harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: institution harvester_local_overwrite: place_of_pub harvester_local_overwrite: pages harvester_local_overwrite: creators_halaffid oai_lastmod: 2023-08-29T14:10:56Z oai_set: tse site: ut1 citation: Daouia, Abdelaati , Stupfler, Gilles Claude and Usseglio-Carleve, Antoine (2022) Inference for extremal regression with dependent heavy-tailed data. TSE Working Paper, n. 22-1324, Toulouse document_url: https://publications.ut-capitole.fr/id/eprint/45033/1/wp_tse_1324.pdf