Huiyan Sang

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Multivariate Max-Stable Processes for Extreme Values
26 October 2017 from 4:00 PM to 5:00 PM
201 Thomas Building
Contact Name
Lorey Burghard
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Analysis of spatial extremes are currently based on univariate processes. Max-stable processesallow to model and explicitly quantify the spatial dependence of extremes, therefore they are widely adopted in the applications. For a better understanding of extreme events of real processes, such as environmental phenomena, it may be useful to simultaneously study several spatial variables. To this end, we extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. In particular, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. Then, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extreme-value, the Schlather extremal-Gaussian and extremal-t, and the Brown–Resnick models. Inferential aspects for those models based on composite likelihoods are developed. We show the results of various Monte Carlo simulations and of an application to a dataset of monthly wind speed and wind gust in Oklahoma, U.S.A., highlighting the utility of working with multivariate models in contrast to the univariate case.

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