Flexible and Fast Spatial Return Level Estimation Via a Spatially Fused Penalty

Danielle Sass, Bo Li, Brian J. Reich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and dependent when they are nearby. An important goal of extremes modeling is to estimate the T-year return level. Among the methods suitable for modeling spatial extremes, perhaps the simplest and fastest approach is the spatial generalized extreme value (GEV) distribution and the spatial generalized Pareto distribution (GPD) that assume marginal independence and only account for dependence through the parameters. Despite the simplicity, simulations have shown that return level estimation using the spatial GEV and spatial GPD still provides satisfactory results compared to max-stable processes, which are asymptotically justified models capable of representing spatial dependence among extremes. However, the linear functions used to model the spatially varying coefficients are restrictive and may be violated. We propose a flexible and fast approach based on the spatial GEV and spatial GPD by introducing fused lasso and fused ridge penalty for parameter regularization. This enables improved return level estimation for large spatial extremes compared to the existing methods. Supplemental files for this article are available online.
Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
StatePublished - 2021
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-08-19
Acknowledged KAUST grant number(s): grant no. 3800.2
Acknowledgements: Li acknowledges partial support from the NSF grants AGS-1602845 and DMS-1830312. Reich acknowledges partial support from The King Abdullah University of Science and Technology (grant no. 3800.2) and National Institutes of Health (NIH grant no. R01ES027892).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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