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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