Geostatistics of Dependent and Asymptotically Independent Extremes

Mathematical Geosciences

Volumn 45, Issue 5, 2013, Pages 511-529

  Davison, A C ^a   Huser, R ^a   Thibaud, E ^a  

^a EPFL   (Switzerland)

Author keywords

Asymptotic independence; Brown Resnick process; Gaussian process; Generalised Pareto distribution; Max stable process; Statistics of extremes

Indexed keywords

ASYMPTOTIC INDEPENDENCE; GAUSSIAN PROCESSES; GENERALISED PARETO DISTRIBUTIONS; MAX-STABLE PROCESS; STATISTICS OF EXTREMES;

FOOD SUPPLY; GAUSSIAN NOISE (ELECTRONIC); STABILITY CRITERIA;

GAUSSIAN DISTRIBUTION;

CATASTROPHIC EVENT; FOOD SECURITY; GAUSSIAN METHOD; GEOSTATISTICS; MATHEMATICAL ANALYSIS; MODEL TEST; MODEL VALIDATION; NUMERICAL MODEL; PRECIPITATION ASSESSMENT; RAINFALL; SPATIAL ANALYSIS; SUSTAINABILITY; TEMPERATURE PROFILE; WINTER;

EID: 84879928321     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-013-9469-y     Document Type: Article

References (79)

1. Banerjee S, Carlin B, Gelfand A (2004) Hierarchical modeling and analysis for spatial data. Chapman and Hall/CRC, New York.
2. Beirlant J, Goegebeur Y, Teugels J, Segers J (2004) Statistics of extremes: theory and applications. Wiley, New York.
3. Blanchet J, Davison AC (2011) Spatial modelling of extreme snow depth. Ann Appl Stat 5: 1699-1725.
4. Bortot P, Coles SG, Tawn JA (2000) The multivariate Gaussian tail model: an application to oceanographic data. Appl Stat 49: 31-49.
5. Brown BM, Resnick SI (1977) Extreme values of independent stochastic processes. J Appl Probab 14: 732-739.
6. Buishand TA, de Hann L, Zhou C (2008) On spatial extremes: with application to a rainfall problem. Ann Appl Stat 2: 624-642.
7. Casson E, Coles SG (1999) Spatial regression models for extremes. Extremes 1: 449-468.
8. Chavez-Demoulin V, Davison AC, Frossard L (2011) Discussion of "Threshold modelling of spatially-dependent non-stationary extremes with application to hurricane-induced wave heights" by P. J. Northrop and P. Jonathan. Environmetrics 22: 810-812.
9. Coles SG (2001) An introduction to statistical modeling of extreme values. Springer, London.
10. Coles SG, Casson E (1998) Extreme value modelling of hurricane wind speeds. Struct Saf 20: 283-296.
11. Coles SG, Pauli F (2002) Models and inference for uncertainty in extremal dependence. Biometrika 89: 183-196.
12. Coles SG, Heffernan JE, Tawn JA (1999) Dependence measures for extreme value analyses. Extremes 2: 339-365.
13. Cooley D, Nychka D, Naveau P (2007) Bayesian spatial modeling of extreme precipitation return levels. J Am Stat Assoc 102: 824-840.
14. Cooley D, Cisewski J, Erhardt RJ, Jeon S, Mannshardt E, Omolo BO, Sun Y (2012a) A survey of spatial extremes: measuring spatial dependence and modeling spatial effects. REVSTAT Stat J 10: 135-165.
15. Cooley D, Davis RA, Naveau P (2012b) Approximating the conditional density given large observed values via a multivariate extremes framework with application to environmental data. Ann Appl Stat 6: 1406-1429.
16. Cressie NAC (1993) Statistics for spatial data. Wiley, New York.
17. Cressie NAC, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New York.
18. Das B, Resnick SI (2011) Conditioning on an extreme component: model consistency with regular variation on cones. Bernoulli 17: 226-252.
19. Davis RA, Mikosch T (2010) The extremogram: a correlogram for extreme events. Bernoulli 15: 977-1009.
20. Davis RA, Yau CY (2011) Comments on pairwise likelihood in time series models. Stat Sin 21: 255-277.
21. Davison AC, Gholamrezaee MM (2012) Geostatistics of extremes. Proc R Soc Lond Ser A 468: 581-608.
22. Davison AC, Smith RL (1990) Models for exceedances over high thresholds (with Discussion). J R Stat Soc, Ser B 52: 393-442.
23. Davison AC, Padoan SA, Ribatet M (2012) Statistical modelling of spatial extremes (with Discussion). Stat Sci 27: 161-186.
24. de Haan L (1984) A spectral representation for max-stable processes. Ann Probab 12: 1194-1204.
25. de Haan L, Ferreira A (2006) Extreme value theory: an introduction. Springer, New York.
26. de Haan L, Resnick SI (1977) Limit theory for multivariate sample extremes. Z Wahrscheinlichkeitstheor Verw Geb 40: 317-337.
27. Diggle PJ, Ribeiro PJ (2007) Model-based geostatistics. Springer, New York.
28. Engelke S, Malinowski A, Kabluchko Z, Schlather M (2012) Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. arXiv: 1207. 6886v2 [stat. ME].
29. Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Math Proc Camb Philos Soc 24: 180-190.
30. Fougères A-L, Soulier P (2012) Estimation of conditional laws given an extremal component. Extremes 15: 1-34.
31. Galambos J (1987) The asymptotic theory of extreme order statistics, 2nd edn. Krieger, Melbourne.
32. Genton MG, Ma Y, Sang H (2011) On the likelihood function of Gaussian max-stable processes. Biometrika 98: 481-488.
33. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York.
34. Heffernan JE, Resnick SI (2007) Limit laws for random vectors with an extreme component. Ann Appl Probab 17: 537-571.
35. Heffernan JE, Tawn JA (2004) A conditional approach for multivariate extreme values (with Discussion). J R Stat Soc, Ser B 66: 497-546.
36. Hosking JRM, Wallis JR (1987) Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29: 339-349.
37. Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27: 251-261.
38. Hsing T (1987) On the characterization of certain point processes. Stoch Process Appl 26: 297-316.
39. Hsing T, Hüsler J, Leadbetter MR (1988) On the exceedance point process for a stationary sequence. Probab Theory Relat Fields 78: 97-112.
40. Huser R, Davison AC (2013, to appear) Space-time modelling of extreme events. J R Stat Soc, Ser B.
41. Huser R, Davison AC (2013) Composite likelihood estimation for the Brown-Resnick process. Biometrika 100: 511-518.
42. Jeon S, Smith RL (2012) Dependence structure of spatial extremes using threshold approach. arXiv: 1209. 6344v1 [stat. ME].
43. Kabluchko Z, Schlather M (2010) Ergodic properties of max-infinitely divisible processes. Stoch Process Appl 120: 281-295.
44. Kabluchko Z, Schlather M, De Haan L (2009) Stationary max-stable fields associated to negative definite functions. Ann Probab 37: 2042-2065.
45. Keef C, Tawn JA, Svensson C (2009) Spatial risk assessment for extreme river flows. Appl Stat 58: 601-618.
46. Keef C, Tawn JA, Lamb R (2013) Estimating the probability of widespread flood events. Environmetrics 24: 13-21.
47. Leadbetter MR (1991) On a basis for 'peaks over threshold' modelling. Stat Probab Lett 12: 357-362.
48. Leadbetter MR, Lindgren G, Rootzén H (1983) Extremes and related properties of random sequences and processes. Springer, New York.
49. Ledford AW, Tawn JA (1996) Statistics for near independence in multivariate extreme values. Biometrika 83: 169-187.
50. Ledford AW, Tawn JA (1997) Modelling dependence within joint tail regions. J R Stat Soc, Ser B 59: 475-499.
51. Ledford AW, Tawn JA (2003) Diagnostics for dependence within time series extremes. J R Stat Soc, Ser B 65: 521-543.
52. Martins E, Stedinger J (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resour Res 36: 737-744.
53. Naveau P, Guillou A, Cooley D, Diebolt J (2009) Modelling pairwise dependence of maxima in space. Biometrika 96: 1-17.
54. Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York.
55. Oesting M, Kabluchko Z, Schlather M (2012) Simulation of Brown-Resnick processes. Extremes 15: 89-107.
56. Padoan SA, Ribatet M, Sisson SA (2010) Likelihood-based inference for max-stable processes. J Am Stat Assoc 105: 263-277.
57. Ramos A, Ledford AW (2009) A new class of models for bivariate joint tails. J R Stat Soc, Ser B 71: 219-241.
58. Ramos A, Ledford AW (2011) An alternative point process framework for modeling multivariate extreme values. Commun Stat, Theory Methods 40: 2205-2224.
59. Reich BJ, Shaby BA (2012) A hierarchical max-stable spatial model for extreme precipitation. Ann Appl Stat 6: 1430-1451.
60. Resnick SI (2006) Heavy-tail phenomena: probabilistic and statistical modeling. Springer, New York.
61. Ribatet M (2011) SpatialExtremes: modelling spatial extremes. R package version 1. 8-5.
62. Ribatet M, Cooley D, Davison AC (2012) Bayesian inference from composite likelihoods, with an application to spatial extremes. Stat Sin 22: 813-845.
63. Salmon F (2009) Recipe for disaster: the formula that killed Wall Street. http://www. wired. com/techbiz/it/magazine/17-03/wp_quant?currentPage=al. Accessed on 6 March 2013.
64. Sang H, Gelfand AE (2009) Hierarchical modeling for extreme values observed over space and time. Environ Ecol Stat 16: 407-426.
65. Sang H, Gelfand AE (2010) Continuous spatial process models for spatial extreme values. J Agric Biol Environ Stat 15: 49-65.
66. Schlather M (2002) Models for stationary max-stable random fields. Extremes 5: 33-44.
67. Schlather M, Tawn JA (2003) A dependence measure for multivariate and spatial extreme values: properties and inference. Biometrika 90: 139-156.
68. Shaby BA, Reich BJ (2012) Bayesian spatial extreme value analysis to assess the changing risk of concurrent high temperatures across large portions of European cropland. Environmetrics 23: 638-648.
69. Shang H, Yan J, Zhang X (2011) El Niño-Southern Oscillation influence on winter maximum daily precipitation in California in a spatial model. Water Resour Res 47: W11507.
70. Smith RL (1989) Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone (with Discussion). Stat Sci 4: 367-393.
71. Smith RL (1990) Max-stable processes and spatial extremes. http://www. stat. unc. edu/postscript/rs/spatex. pdf.
72. Stephenson A, Tawn JA (2005) Exploiting occurrence times in likelihood inference for componentwise maxima. Biometrika 92: 213-227.
73. Thibaud E, Mutzner R, Davison AC (2013, to appear) Threshold modeling of extreme spatial rainfall. Water Resour Res. doi: 10. 1002/wrcr. 20329.
74. Varin C, Vidoni P (2005) A note on composite likelihood inference and model selection. Biometrika 92: 519-528.
75. Varin C, Reid N, Firth D (2011) An overview of composite likelihood methods. Stat Sin 21: 5-42.
76. Wackernagel H (2003) Multivariate geostatistics: an introduction with applications, 3rd edn. Springer, New York.
77. Wadsworth JL, Tawn JA (2012) Dependence modelling for spatial extremes. Biometrika 99: 253-272.
78. Wadsworth JL, Tawn JA (2013, to appear) Efficient inference for spatial extreme value processes associated to log-Gaussian random functions. Biometrika.
79. Westra S, Sisson SA (2011) Detection of non-stationarity in precipitation extremes using a max-stable process model. J Hydrol 406: 119-128.