Spatial dependence and space-time trend in extreme events

John Einmahl, Ana Ferreira, L.F.M. de Haan, C. Neves, Chen Zhou

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The
non-stationarity over time and space is controlled via the scedasis (tail scale)
in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted
sequential tail empirical process and the weighted tail quantile process based
on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a
pseudo-maximum likelihood procedure based on pooling all (non-stationary
and dependent) observations. Our leading example and application is rainfall
in Northern Germany.
Original languageEnglish
JournalThe Annals of Statistics
Publication statusAccepted/In press - Mar 2021

Keywords

  • multivariate extreme value statistics
  • non-identical distributions
  • sequential tail empirical process
  • testing

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