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On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions

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  • Jennifer L. Wadsworth

Abstract

Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood. However, some studies have noted bias when performing high-dimensional inference that incorporates such event information, particularly when dependence is weak. We elucidate this phenomenon, showing that for unbiased inference in moderate dimensions, dimension $d$ should be of a magnitude smaller than the square root of the number of vectors over which one takes the componentwise maximum. A bias reduction technique is suggested and illustrated on the extreme-value logistic model.

Suggested Citation

  • Jennifer L. Wadsworth, 2015. "On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions," Biometrika, Biometrika Trust, vol. 102(3), pages 705-711.
  • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:705-711.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv029
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    References listed on IDEAS

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    1. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    2. Emeric Thibaud & Thomas Opitz, 2015. "Efficient inference and simulation for elliptical Pareto processes," Biometrika, Biometrika Trust, vol. 102(4), pages 855-870.
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    Cited by:

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    2. Alexis Bienvenüe & Christian Y. Robert, 2017. "Likelihood Inference for Multivariate Extreme Value Distributions Whose Spectral Vectors have known Conditional Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 130-149, March.

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