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

Area of Science:

• Climate science
• Extreme value theory
• Statistical modeling

Background:

• Spatial extremes are common in climate data, necessitating accurate T-year return level estimation.
• Existing spatial generalized extreme value (GEV) and generalized Pareto distribution (GPD) models offer simplicity but have limitations in capturing complex spatial dependencies.
• Max-stable processes are theoretically sound for spatial dependence but can be computationally intensive.

Purpose of the Study:

• To develop a flexible and fast approach for modeling spatial extremes.
• To improve the estimation of T-year return levels for large spatial extremes.
• To overcome the limitations of linear functions in modeling spatially varying coefficients.

Main Methods:

• Utilizing spatial GEV and spatial GPD distributions.
• Introducing fused lasso and fused ridge penalties for parameter regularization.
• Applying these penalized methods to model spatially varying coefficients.

Main Results:

• The proposed method demonstrates improved return level estimation for spatial extremes.
• Simulations indicate satisfactory performance compared to existing methods, including max-stable processes.
• The penalized approach offers greater flexibility than traditional linear models for spatially varying coefficients.

Conclusions:

• The fused penalized spatial GEV and GPD approach provides a flexible and efficient alternative for extreme value analysis.
• This method enhances the accuracy of T-year return level estimation in the presence of spatial dependence.
• The findings have significant implications for climate risk assessment and adaptation strategies.