Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. Engelke, S., Malinowski, A., Kabluchko, Z., & Schlather, M. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77(1):239–265, 2015. doi abstract bibtex Estimation of extreme-value parameters from observations in the max-domain of attraction (MDA) of a multivariate max-stable distribution commonly uses aggregated data such as block maxima. Since we expect that additional information is contained in the non-aggregated, single \textquotedbllarge\textquotedbl observations, we introduce a new approach of inference based on a multivariate peaks-over-threshold method. We show that for any process in the MDA of the frequently used Hüsler-Reiss model or its spatial extension, the Brown-Resnick process, suitably defined conditional increments asymptotically follow a multivariate Gaussian distribution. This leads to computationally efficient estimates of the Hüsler-Reiss parameter matrix. Further, the results enable parametric inference for Brown-Resnick processes. A simulation study compares the performance of the new estimators to 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.
@article{Engelke2014Estimation,
abstract = {Estimation of extreme-value parameters from observations in the max-domain of
attraction (MDA) of a multivariate max-stable distribution commonly uses
aggregated data such as block maxima. Since we expect that additional
information is contained in the non-aggregated, single {\textquotedbl}large{\textquotedbl} observations, we
introduce a new approach of inference based on a multivariate
peaks-over-threshold method. We show that for any process in the MDA of the
frequently used H{\"u}sler-Reiss model or its spatial extension, the
Brown-Resnick process, suitably defined conditional increments asymptotically
follow a multivariate Gaussian distribution. This leads to computationally
efficient estimates of the H{\"u}sler-Reiss parameter matrix. Further, the
results enable parametric inference for Brown-Resnick processes. A simulation
study compares the performance of the new estimators to 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.},
author = {Engelke, Sebastian and Malinowski, Alexander and Kabluchko, Zakhar and Schlather, Martin},
year = {2015},
title = {Estimation of {H}{\"u}sler-{Reiss} distributions and {Brown-Resnick} processes},
keywords = {phd;stat},
pages = {239--265},
volume = {77},
number = {1},
issn = {13697412},
journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
doi = {10.1111/rssb.12074},
howpublished = {refereed}
}
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