An integrated functional Weissman estimator for conditional extreme quantiles
It is well-known that estimating extreme quantiles, namely, quantiles lying beyond the range of the available data, is a nontrivial problem that involves the analysis of tail behavior through the estimation of the extreme-value index. For heavy-tailed distributions, on which this paper focuses, the...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatica
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41028/ |
| _version_ | 1848796180889206784 |
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| author | Gardes, Laurent Stupfler, Gilles |
| author_facet | Gardes, Laurent Stupfler, Gilles |
| author_sort | Gardes, Laurent |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | It is well-known that estimating extreme quantiles, namely, quantiles lying beyond the range of the available data, is a nontrivial problem that involves the analysis of tail behavior through the estimation of the extreme-value index. For heavy-tailed distributions, on which this paper focuses, the extreme-value index is often called the tail index and extreme quantile estimation typically involves an extrapolation procedure. Besides, in various applications, the random variable of interest can be linked to a random covariate. In such a situation, extreme quantiles and the tail index are functions of the covariate and are referred to as conditional extreme quantiles and the conditional tail index, respectively. The goal of this paper is to provide classes of estimators of these quantities when there is a functional (i.e. possibly infinite-dimensional) covariate. Our estimators are obtained by combining regression techniques with a generalization of a classical extrapolation formula. We analyze the asymptotic properties of these estimators, and we illustrate the finite-sample performance of our conditional extreme antile estimator on a simulation study and on a real chemometric data set. |
| first_indexed | 2025-11-14T19:43:53Z |
| format | Article |
| id | nottingham-41028 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:43:53Z |
| publishDate | 2017 |
| publisher | Instituto Nacional de Estatica |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410282017-10-13T01:37:19Z https://eprints.nottingham.ac.uk/41028/ An integrated functional Weissman estimator for conditional extreme quantiles Gardes, Laurent Stupfler, Gilles It is well-known that estimating extreme quantiles, namely, quantiles lying beyond the range of the available data, is a nontrivial problem that involves the analysis of tail behavior through the estimation of the extreme-value index. For heavy-tailed distributions, on which this paper focuses, the extreme-value index is often called the tail index and extreme quantile estimation typically involves an extrapolation procedure. Besides, in various applications, the random variable of interest can be linked to a random covariate. In such a situation, extreme quantiles and the tail index are functions of the covariate and are referred to as conditional extreme quantiles and the conditional tail index, respectively. The goal of this paper is to provide classes of estimators of these quantities when there is a functional (i.e. possibly infinite-dimensional) covariate. Our estimators are obtained by combining regression techniques with a generalization of a classical extrapolation formula. We analyze the asymptotic properties of these estimators, and we illustrate the finite-sample performance of our conditional extreme antile estimator on a simulation study and on a real chemometric data set. Instituto Nacional de Estatica 2017-02-21 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/41028/1/gardes_stupfler_final.pdf Gardes, Laurent and Stupfler, Gilles (2017) An integrated functional Weissman estimator for conditional extreme quantiles. Revstat Statistical Journal . ISSN 1645-6726 (In Press) Heavy-tailed distribution functional random covariate extreme quantile tail index asymptotic normality |
| spellingShingle | Heavy-tailed distribution functional random covariate extreme quantile tail index asymptotic normality Gardes, Laurent Stupfler, Gilles An integrated functional Weissman estimator for conditional extreme quantiles |
| title | An integrated functional Weissman estimator for conditional
extreme quantiles |
| title_full | An integrated functional Weissman estimator for conditional
extreme quantiles |
| title_fullStr | An integrated functional Weissman estimator for conditional
extreme quantiles |
| title_full_unstemmed | An integrated functional Weissman estimator for conditional
extreme quantiles |
| title_short | An integrated functional Weissman estimator for conditional
extreme quantiles |
| title_sort | integrated functional weissman estimator for conditional
extreme quantiles |
| topic | Heavy-tailed distribution functional random covariate extreme quantile tail index asymptotic normality |
| url | https://eprints.nottingham.ac.uk/41028/ |