A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects

Daniel Cooley*, Jessi Cisewski, Robert J. Erhardt, Soyoung Jeon, Elizabeth Mannshardt, Bernard Oguna Omolo, Ying Sun

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

59 Scopus citations

Abstract

We survey the current practice of analyzing spatial extreme data, which lies at the intersection of extreme value theory and geostatistics. Characterizations of multivariate max-stable distributions typically assume specific univariate marginal distributions, and their statistical applications generally require capturing the tail behavior of the margins and describing the tail dependence among the components. We review current methodology for spatial extremes analysis, discuss the extension of the finite-dimensional extremes framework to spatial processes, review spatial dependence metrics for extremes, survey current modeling practice for the task of modeling marginal distributions, and then examine max-stable process models and copula approaches for modeling residual spatial dependence after accounting for marginal effects.

Original languageEnglish (US)
Pages (from-to)135-165
Number of pages31
JournalRevstat Statistical Journal
Volume10
Issue number1
StatePublished - Mar 1 2012

Keywords

  • Copula
  • Extremal coefficient
  • Hierarchical model
  • Madogram
  • Max-stable process
  • Multi-variate extreme value distribution

ASJC Scopus subject areas

  • Statistics and Probability

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