Simple models for multivariate regular variation and the Hüsler–Reiß Pareto distribution

Zhen Wai Olivier Ho and Clément Dombry

Journal of Multivariate Analysis, 2019, vol. 173, issue C, 525-550

Abstract: We revisit multivariate extreme-value theory modeling by emphasizing multivariate regular variation and a multivariate version of Breiman’s Lemma. This allows us to recover in a simple framework the most popular multivariate extreme-value distributions, such as the logistic, negative logistic, Dirichlet, extremal- t and Hüsler–Reiß models. We then focus on the Hüsler–Reiß Pareto model and its surprising exponential family property. After a thorough study of this exponential family structure, we focus on maximum likelihood estimation: we prove the existence of asymptotically normal maximum likelihood estimators and provide simulation experiments assessing their finite-sample properties. We also consider the generalized Hüsler–Reiß Pareto model with different tail indices and a likelihood ratio test for discriminating constant tail index versus varying tail indices.

Keywords: Exponential family; Extreme value theory; Maximum likelihood estimation; Regular variations (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:173:y:2019:i:c:p:525-550

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DOI: 10.1016/j.jmva.2019.04.008

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