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1 results

  • One-component regular variation and graphical modeling of extremes

  • Part of
  • Adrien Hitz, Robin Evans
  • Journal:
    Journal of Applied Probability / Volume 53 / Issue 3 / September 2016
    Published online by Cambridge University Press:
    24 October 2016, pp. 733-746
    Print publication:
    September 2016

  • The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize the Hammersley–Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails.