Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 77, Issue 1, Pages 239-265Publisher
WILEY
DOI: 10.1111/rssb.12074
Keywords
Extreme value theory; Max-stable process; Peaks-over-threshold method; Poisson point process; Spectral density
Categories
Funding
- Deutsche Telekom Stiftung
- Swiss National Science Foundation [200021-140633]
- German Science Foundation, Research Training Group [1644]
- Volkswagen Stiftung within the project 'WEX-MOP'
- Swiss National Science Foundation (SNF) [200021_140633] Funding Source: Swiss National Science Foundation (SNF)
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Estimation of extreme value parameters from observations in the max-domain of attraction of a multivariate max-stable distribution commonly uses aggregated data such as block maxima. Multivariate peaks-over-threshold methods, in contrast, exploit additional information from the non-aggregated 'large' observations. We introduce an approach based on peaks over thresholds that provides several new estimators for processes eta in the max-domain of attraction of the frequently used Husler-Reiss model and its spatial extension: Brown-Resnick processes. The method relies on increments eta(.) - eta t(0)/conditional on eta t(0)/exceeding a high threshold, where t(0) is a fixed location. When the marginals are standardized to the Gumbel distribution, these increments asymptotically form a Gaussian process resulting in computationally simple estimates of the Husler-Reiss parameter matrix and particularly enables parametric inference for Brown-Resnick processes based on (high dimensional) multivariate densities. This is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities. A simulation study compares the performance of the new estimators with other commonly used methods. As an application, we fit a non-isotropic Brown-Resnick process to the extremes of 12-year data of daily wind speed measurements.
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