On extreme quantile region estimation under heavy-tailed elliptical distributions

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2024-07
Major/Subject
Mcode
Degree programme
Language
en
Pages
20
Series
Journal of Multivariate Analysis, Volume 202, pp. 1-20
Abstract
Consider the estimation of an extreme quantile region corresponding to a very small probability. Estimation of extreme quantile regions is important but difficult since extreme regions contain only a few or no observations. In this article, we propose an affine equivariant extreme quantile region estimator for heavy-tailed elliptical distributions. The estimator is constructed by extending a well-known univariate extreme quantile estimator. Consistency of the estimator is proved under estimated location and scatter. The practicality of the developed estimator is illustrated with simulations and a real data example.
Description
Publisher Copyright: © 2024 The Author(s)
Keywords
Elliptical distribution, Extreme quantile estimation, Heavy-tailed distribution, Multivariate quantile
Other note
Citation
Pere, J, Ilmonen, P & Viitasaari, L 2024, ' On extreme quantile region estimation under heavy-tailed elliptical distributions ', Journal of Multivariate Analysis, vol. 202, 105314, pp. 1-20 . https://doi.org/10.1016/j.jmva.2024.105314