Modeling Spatial Processes with Unknown Extremal Dependence Class

References

• Azzalini, A., and Dalla Valle, A. (1996), “The Multivariate Skew-Normal Distribution,” Biometrika, 83, 715–726.
   Web of Science ®Google Scholar
• Castruccio, S., Huser, R., and Genton, M. G. (2016), “High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes,” Journal of Computational and Graphical Statistics, 25, 1212–1229.
   Web of Science ®Google Scholar
• Coles, S. G., Heffernan, J., and Tawn, J. A. (1999), “Dependence Measures for Extreme Value Analyses,” Extremes, 2, 339–365.
   Google Scholar
• Coles, S. G., and Pauli, F. (2002), “Models and Inference for Uncertainty in Extremal Dependence,” Biometrika, 89, 183–196.
   Web of Science ®Google Scholar
• Coles, S. G., and Tawn, J. A. (1991), “Modelling Extreme Multivariate Events,” Journal of the Royal Statistical Society, Series B, 53, 377–392.
   Google Scholar
• Cooley, D. S., Cisewski, J., Erhardt, R. J., Jeon, S., Mannshardt-Shamseldin, E. C., Omolo, B. O., and Sun, Y. (2012), “A Survey of Spatial Extremes: Measuring Spatial Dependence and Modeling Spatial Effects,” REVSTAT, 10, 135–165.
   Web of Science ®Google Scholar
• Davison, A. C., Huser, R., and Thibaud, E. (2013), “Geostatistics of Dependent and Asymptotically Independent Extremes,” Mathematical Geoscience, 45, 511–529.
   Web of Science ®Google Scholar
• Davison, A. C., and Huser, R. (2015), “Statistics of Extremes,” Annual Review of Statistics and its Application, 2, 203–235.
   Web of Science ®Google Scholar
• Davison, A. C., Padoan, S., and Ribatet, M. (2012), “Statistical Modelling of Spatial Extremes” (with discussion), Statistical Science, 27, 161–186.
   Web of Science ®Google Scholar
• de Fondeville, R., and Davison, A. C. (2018), “High-dimensional Peaks-Over-Threshold Inference,” Preprint, ArXiv:1605.08558.
   Google Scholar
• de Haan, L., and Ferreira, A. (2006), Extreme Value Theory: An Introduction, New York: Springer.
   Google Scholar
• Engelke, S., Malinowski, A., Kabluchko, Z., and Schlather, M. (2015), “Estimation of Hüsler–Reiss Distributions and Brown–Resnick Processes,” Journal of the Royal Statistical Society, Series B, 77, 239–265.
   Google Scholar
• Ferreira, A., and de Haan, L. (2014), “The Generalized Pareto process; With a View Towards Application and Simulation,” Bernoulli, 20, 1717–1737.
   Web of Science ®Google Scholar
• Gabda, D., Towe, R., Wadsworth, J. L., and Tawn, J. A. (2012), “Discussion of ‘Statistical Modeling of Spatial Extremes’ by A. C. Davison, S. A. Padoan and M. Ribatet,” Statistical Science, 27, 189–192.
   Web of Science ®Google Scholar
• Huser, R., Davison, A. C., and Genton, M. G. (2016), “Likelihood Estimators for Multivariate Extremes,” Extremes, 19, 79–103.
   Web of Science ®Google Scholar
• Huser, R., Opitz, T., and Thibaud, E. (2017), “Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures,” Spatial Statistics, 21, 166–186.
   Web of Science ®Google Scholar
• Jenkinson, A. F. (1955), “The Frequency Distribution of the Annual Maximum (or Minimum) Values of Meteorological Elements,” Quarterly Journal of the Royal Meteorological Society, 81, 158–171.
   Web of Science ®Google Scholar
• Joe, H. (2015), Dependence Modeling with Copulas, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Krupskii, P., Huser, R., and Genton, M. G. (2018), “Factor Copula Models for Replicated Spatial Data,” Journal of the American Statistical Association, 113, 467–479.
   Web of Science ®Google Scholar
• Ledford, A. W., and Tawn, J. A. (1996), “Statistics for Near Independence in Multivariate Extreme Values,” Biometrika, 83, 169–187.
   Web of Science ®Google Scholar
• Ledford, A. W., and Tawn, J. A. (1997), “Modelling Dependence Within Joint Tail Regions,” Journal of the Royal Statistical Society, Series B, 59, 475–499.
   Google Scholar
• Opitz, T. (2016), “Modeling Asymptotically Independent Spatial Extremes Based on Laplace Random Fields,” Spatial Statistics, 16, 1–18.
   Web of Science ®Google Scholar
• Padoan, S., Ribatet, M., and Sisson, S. (2010), “Likelihood-Based Inference for Max-stable Processes,” Journal of the American Statistical Association, 105, 263–277.
   Web of Science ®Google Scholar
• Politis, D. N., and Romano, J. P. (1994), “The Stationary Bootstrap,” Journal of the American Statiatical Association, 89, 1303–1313.
   Web of Science ®Google Scholar
• Resnick, S. I. (2002), “Hidden Regular Variation, Second Order Regular Variation and Asymptotic Independence,” Extremes, 5, 303–336.
   Google Scholar
• Rootzén, H., Segers, J., and Wadsworth, J. L. (2018), “Multivariate Generalized Pareto Distributions: Parametrizations, Representations, and Properties,” Journal of Multivariate Analysis, 165, 117–131.
   Web of Science ®Google Scholar
• Segers, J. (2012), “Max-Stable Models for Multivariate Extremes,” REVSTAT, 10, 61–82.
   Web of Science ®Google Scholar
• Sklar, A. (1959), “Fonctions De Répartition à n Dimensions et Leurs Marges,” Publications de l’institut de Statistique de l’Université de Paris, 8, 229–231.
   Google Scholar
• Smith, R. L., Tawn, J. A., and Coles, S. G. (1997), “Markov Chain Models for Threshold Exceedances,” Biometrika, 84, 249–268.
   Web of Science ®Google Scholar
• Thibaud, E., and Opitz, T. (2015), “Efficient Inference and Simulation for Elliptical Pareto Processes,” Biometrika, 102, 855–870.
   Web of Science ®Google Scholar
• Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
   Web of Science ®Google Scholar
• von Mises, R. (1936), “La Distribution de la Plus Grande de n Valeurs,” Rev. Math. Union Interbalcanique 1, 141–160.
   Google Scholar
• Wadsworth, J. L., Tawn, J. A., Davison, A. C., and Elton, D. M. (2017), “Modelling Across Extremal Dependence Classes,” Journal of the Royal Statistical Society, Series B, 79, 149–175.
   Google Scholar
• Wadsworth, J. L., and Tawn, J. A. (2012), “Dependence Modelling for Spatial Extremes,” Biometrika, 99, 253–272.
   Web of Science ®Google Scholar
• Wadsworth, J. L., and Tawn, J. A. (2014), “Efficient Inference for Spatial Extreme Value Processes Associated to Log-Gaussian Random Functions,” Biometrika, 101, 1–15.
   Web of Science ®Google Scholar