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dc.contributor.authorZhong, Peng
dc.contributor.authorHuser, Raphaël
dc.contributor.authorOpitz, Thomas
dc.date.accessioned2021-03-10T06:44:08Z
dc.date.available2021-03-10T06:44:08Z
dc.date.issued2021-02-28
dc.identifier.urihttp://hdl.handle.net/10754/668027
dc.description.abstractMax-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the componentwise maximum of random functions drawn from a Poisson point process defined on a suitable functions space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, we here develop theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. We present the results of a simulation study highlighting that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a byproduct, we also develop here new max-id models, which can be represented as pointwise maxima of general location scale mixtures, and which possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2103.00533.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectAdaptive rejection sampling
dc.subjectExact simulation
dc.subjectExtremal function
dc.subjectMaxinfinitely divisible process
dc.subjectMax-stable process.
dc.titleExact Simulation of Max-Infinitely Divisible Processes
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics
dc.contributor.departmentStatistics Program
dc.eprint.versionPre-print
dc.identifier.arxivid2103.00533
kaust.personZhong, Peng
kaust.personHuser, Raphaël
kaust.personOpitz, Thomas
refterms.dateFOA2021-03-10T06:44:35Z


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