On extreme quantile region estimation under heavy-tailed elliptical distributions

Jaakko Pere, Pauliina Ilmonen and Lauri Viitasaari

Journal of Multivariate Analysis, 2024, vol. 202, issue C

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.

Keywords: Elliptical distribution; Extreme quantile estimation; Heavy-tailed distribution; Multivariate quantile (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.jmva.2024.105314

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