Local Likelihood Estimation of Complex Tail Dependence Structures, Applied to U.S. Precipitation Extremes

Abstract

To disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous United States (U.S.), we propose a flexible local approach based on factor copula models. Our subasymptotic spatial modeling framework yields nontrivial tail dependence structures, with a weakening dependence strength as events become more extreme; a feature commonly observed with precipitation data but not accounted for in classical asymptotic extreme-value models. To estimate the local extremal behavior, we fit the proposed model in small regional neighborhoods to high threshold exceedances, under the assumption of local stationarity, which allows us to gain in flexibility. By adopting a local censored likelihood approach, we make inference on a fine spatial grid, and we perform local estimation by taking advantage of distributed computing resources and the embarrassingly parallel nature of this estimation procedure. The local model is efficiently fitted at all grid points, and uncertainty is measured using a block bootstrap procedure. We carry out an extensive simulation study to show that our approach can adequately capture complex, nonstationary dependencies, in addition, our study of U.S. winter precipitation data reveals interesting differences in local tail structures over space, which has important implications on regional risk assessment of extreme precipitation events. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Factor copula model
• Local likelihood
• Nonstationarity
• Spatial extremes
• Threshold exceedance

Acknowledgments

We thank Luigi Lombardo (University of Twente) for his cartographic support and Eduardo González (KAUST) for his computational support. We extend our thanks to Dan Cooley (Colorado State University) for helpful comments and suggestions. Support from the KAUST Supercomputing Laboratory and access to Shaheen is also gratefully acknowledged. We are particularly grateful to the two referees for their comments and suggestions that have led to a much improved version of this article.

ORCID

Daniela Castro-Camilo ≪INLINE FIGURE≫ https://orcid.org/0000-0002-7536-4613

Raphaël Huser ≪INLINE FIGURE≫ https://orcid.org/0000-0002-1228-2071