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    Exact Simulation of Max-Infinitely Divisible Processes

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    Type
    Preprint
    Authors
    Zhong, Peng
    Huser, Raphaël cc
    Opitz, Thomas
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics
    Statistics Program
    Date
    2021-02-28
    Permanent link to this record
    http://hdl.handle.net/10754/668027
    
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    Abstract
    Max-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.
    Publisher
    arXiv
    arXiv
    2103.00533
    Additional Links
    https://arxiv.org/pdf/2103.00533.pdf
    Collections
    Preprints; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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