On spatial extremes: With application to a rainfall problem

By T. Buishand, Laurens de Haan, Chen Zhou. 2008

215 citations recorded by the source corpus.

We consider daily rainfall observations at 32 stations in the province of North Holland (the Netherlands) during 30 years. Let T be the total rainfall in this area on one day. An important question is: what is the amount of rainfall T that is exceeded once in 100 years? This is clearly a problem belonging to extreme value theory. Also, it is a genuinely spatial problem. Recently. a theory of extremes of continuous stochastic processes has been developed. Using the ideas of that theory and much computer power (simulations), we have been able to come up with a reasonable answer to the question above.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/8cce8f9152ed21ad56164af1a8cacf5a0ea82c22

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Citations in the corpus

Conditional simulation of max-stable processes (2012, background): “INTRODUCTION Max-stable processes arise naturally when studying extremes of stochastic processes and therefore play a major role in the statistical modelling of spatial extremes (Buishand et al, 2008; Padoan et al., 2010; Davison et al., 2011).”
Asymptotic models and inference for extremes of spatio-temporal data (2010, methodology): “We also note that, the model suggested by Buishand et al. (2008) is a max-stable process conditional on the values of the estimated parameters.”
Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels (2010, methodology): “We refer to (Buishand et al. 2008; Padoan et al. 2009) for applications to the daily rainfalls in the Netherlands and in the USA respectively.”
Bias correction in extreme value statistics with index around zero (2013, unknown): “12 respectively; for daily rainfall in North Holland, The Netherlands, Buishand et al. (2008) obtain a γ estimate at 0.”
Simulation of Brown–Resnick processes (2012, methodology): “Finally, Buishand et al. (2008) and de Haan and Zhou (2008) used Brown–Resnick processes for modelling spatial rainfall.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, background): “1 in Drees, de Haan and Li (2003), allowing one to move from a BM second order condition (such as the one imposed in Bücher and Segers, 2014) to a POT second order condition as in (4.”
Exact simulation of Brown-Resnick random fields at a finite number of locations (2014, background): “[2], de Haan and Zhou [9], Dombry et al.”
Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, background): “Buishand et al. (2008), de Haan and Zhou (2008) and Padoan et al.”
Space–time modelling of extreme events (2012, methodology): “Other models include the Brown–Resnick processes (see Kabluchko and Schlather, 2010), and a Brownian motion model proposed by Buishand et al. (2008), which has the drawback of not being invariant with respect to coordinate axes. Wadsworth and Tawn (2012) generalize these models to hybrids able to ca”
Spatial extremes: Max-stable processes at work (2013, background): “Although some simple representations have been found Buishand et al. (2008); Aulbach et al. (2012); de Haan and Ferreira (2012); Dombry and Ribatet (2013), we are far from being able to use generalized Pareto processes for concrete applications.”
An M‐estimator of spatial tail dependence (2014, background): “Another parametric model for spatial tail dependence is introduced in Buishand et al. (2008).”
Functional regular variations, Pareto processes and peaks over threshold (2015, background): “[5] were interested in the total amount of rain over a catchment T , i.”
Stationary max-stable fields associated to negative definite functions. (2008, methodology): “, td) = |t1| + · · · + |td| was used as a model of extreme spatial rainfall in [6] and [13].”
Conditional sampling for spectrally discrete max-stable random fields (2010, background): “[2], Schlather [22], Schlather and Tawn [23], Cooley et al.”