NDLI: Estimation of spatial max-stable models using threshold exceedances

Content Provider	Springer Nature Link
Author	Bacro, Jean el Gaetan, Carlo
Copyright Year	2013
Abstract	Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed. However modeling block maxima is a wasteful approach provided that other information is available. Moreover an approach based on block maxima, typically annual, is unable to take into account the fact that maxima occur or not simultaneously. If time series of, say, daily data are available, then estimation procedures based on exceedances of a high threshold could mitigate such problems. We focus on two approaches for composing likelihoods based on pairs of exceedances. The first one comes from the tail approximation for bivariate distribution proposed by Ledford and Tawn (Biometrika 83:169–187, 1996) when both pairs of observations exceed the fixed threshold. The second one uses the bivariate extension (Rootzén and Tajvidi in Bernoulli 12:917–930, 2006) of the generalized Pareto distribution which allows to model exceedances when at least one of the components is over the threshold. The two approaches are compared through a simulation study where both processes in a domain of attraction of a max-stable process and max-stable processes are successively considered as time replications, according to different degrees of spatial dependency. Results put forward how the nature of the time replications influences the bias of estimations and highlight the choice of each approach regarding to the strength of the spatial dependencies and the threshold choice.
Starting Page	651
Ending Page	662
Page Count	12
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	24
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2013-05-17
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Composite likelihood Extremal dependence Generalized Pareto distribution Spatial statistics Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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