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On extreme quantile region estimation under heavy-tailed elliptical distributions

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  • Pere, Jaakko
  • Ilmonen, Pauliina
  • Viitasaari, Lauri

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.

Suggested Citation

  • Pere, Jaakko & Ilmonen, Pauliina & Viitasaari, Lauri, 2024. "On extreme quantile region estimation under heavy-tailed elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x24000216
    DOI: 10.1016/j.jmva.2024.105314
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