On extreme quantile region estimation under heavy-tailed elliptical distributions

Jaakko Pere*, Pauliina Ilmonen, Lauri Viitasaari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article number105314
Pages (from-to)1-20
Number of pages20
JournalJournal of Multivariate Analysis
Volume202
DOIs
Publication statusPublished - Jul 2024
MoE publication typeA1 Journal article-refereed

Keywords

  • Elliptical distribution
  • Extreme quantile estimation
  • Heavy-tailed distribution
  • Multivariate quantile

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