Regular conditional distributions of continuous max-infinitely divisible random fields

By Clément Dombry, Fr'ed'eric 'Eyi-Minko. 2013

60 citations recorded by the source corpus.

This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given observations $\{\eta(t_i)=y_i,\ 1\leq i\leq k\}$. Our starting point is the point process representation of max-infinitely divisible processes by Gine, Hahn and Vatan (1990). We carefully analyze the structure of the underlying point process, introduce the notions of extremal function, sub-extremal function and hitting scenario associated to the constraints and derive the associated distributions. This allows us to explicit the conditional distribution as a mixture over all hitting scenarios compatible with the conditioning constraints. This formula extends a recent result by Wang and Stoev (2011) dealing with the case of spectrally discrete max-stable random fields. This paper offers new tools and perspective or prediction in extreme value theory together with numerous potential applications.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/297496bd3e59a4d09912684a68b467974e820838

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Citations in the corpus

Conditional simulation of max-stable processes (2012, background): “Recently, Dombry and Eyi-Minko (2013) provided an explicit theoretical formula for the conditional distributions of max-stable processes.”
Spatial extremes: Max-stable processes at work (2013, unknown): “Recently conditional simulation from max-stable processes has gained some interests with the pioneering work of Wang and Stoev (2011) followed by that of Dombry and Éyi-Minko (2013); Dombry et al. (2013).”
Graphical models for extremes (2018, background): “Exact simulation Exact simulation of a max-stable random vector Z relies on the notion of extremal functions (Dombry and Éyi-Minko, 2013).”