Variograms for spatial max-stable random fields

Brockwell, P.J. and Davis, R.A. (1991). Times Series: Theory and Methods. Springer Verlag.Google Scholar

Chilès, J.-P. and Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty. John Wiley & Sons Inc., New York. A Wiley-Interscience Publication.zbMATHGoogle Scholar

Coles, S. and Casson, E. A. (1999). Spatial regression for extremes. Extremes, 1:339–365.CrossRefGoogle Scholar

Coles, S. and Dixon, M. (1999). Likelihood-based inference for extreme value models. Extremes, 2:523.CrossRefGoogle Scholar

Coles, S. G. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer-Verlag London Ltd., London.zbMATHGoogle Scholar

Cressie, N. A. C. (1993). Statistics for Spatial Data. John Wiley & Sons Inc., New York.zbMATHGoogle Scholar

Davis, R. and Mikosch, T. (2004). Extreme value theory for space-time processes with heavy-tailed distributions. Lecture notes from the MaPhySto Workshop on “Nonlinear Time Series Modeling”, Copenhagen, Denmark.Google Scholar

Davis, R. and Resnick, S. (1993). Prediction of stationary max-stable processes. Ann. of Applied Prob, 3:497–525.zbMATHMathSciNetGoogle Scholar

de Haan, L. and Pereira, T. (2005). Spatial extremes: the stationary case. submitted.Google Scholar

de Haan, L. and Resnick, S. (1977). Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitstheorie, 4:317–337.CrossRefGoogle Scholar

Embrechts, P., Klüppelberg, C., and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, volume 33 of Applications of Mathematics. Springer-Verlag, Berlin. For insurance and finance.zbMATHGoogle Scholar

Fougères, A. (2004). Multivariate extremes. In B. Finkenstadt and H. Rootzen, editor, Extreme Values in Finance, Telecommunications and the Environment, pages 373–388. Chapman and Hall CRC Press, London.Google Scholar

Greenwood, J., Landwehr, J., Matalas, N., and Wallis, J. (1979). Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15:1049–1054.CrossRefGoogle Scholar

Heffernan, J. E. and Tawn, J. A. (2004). A conditional approach for multivariate extreme values. Journal of the Royal Statistical Society, Series B, 66.Google Scholar

Hoskings, J. and Wallis, J. (1987). Parameter and quantile estimation for the Generalized Pareto Distribution. Technometrics, 29:339–349.MathSciNetCrossRefGoogle Scholar

Hoskings, J., Wallis, J., and Wood, E. (1985). Estimation of the generalized extreme-value distribution by the method of probability-weighted-moments. Technometrics, 27:251–261.MathSciNetCrossRefGoogle Scholar

Katz, R., Parlange, M., and Naveau, P. (2002). Extremes in hydrology. Advances in Water Resources, 25:1287–1304.CrossRefGoogle Scholar

Landwher, J., Matalas, N., and Wallis, J. (1979). Probability weighted moments compared with some traditionnal techniques in estimating Gumbel’s parameters and quantiles. Water Resources Research, 15:1055–1064.Google Scholar

Leadbetter, M., Lindgren, G., and Rootzén, H. (1983). Extremes and related properties of random sequences and processes. Springer Verlag, New York.zbMATHGoogle Scholar

Ledford, A. and Tawn, J. (1997). Modelling dependence within joint tail regions. J. R. Statist. Soc., B:475–499.zbMATHMathSciNetCrossRefGoogle Scholar

Matheron, G. (1987). Suffit-il, pour une covariance, d’être de type positif? Sciences de la Terre, série informatique géologique, 26:51–66.Google Scholar

Naveau, P., Poncet, P., and Cooley, D. (2005). First-order variograms for extreme bivariate random vectors. Submitted.Google Scholar

Poncet, P. (2004). Théorie des valeurs extrêmes: vers le krigeage et le downscaling par l’introduction du madogramme. Ecole nationale supérieure des Mines de Paris, Paris, France.Google Scholar

Resnick, S. (1987). Extreme Values, Regular Variation, and Point Processes. Springer-Verlag, New York.zbMATHGoogle Scholar

Schlather, M. (2002). Models for stationary max-stable random fields. Extremes, 5(1):33–44.zbMATHMathSciNetCrossRefGoogle Scholar

Schlather, M. and Tawn, J. (2003). A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika, 90:139–156.zbMATHMathSciNetCrossRefGoogle Scholar

Smith, R. (1990). Max-stable processes and spatial extremes. Unpublished manusript.Google Scholar

Smith, R. (2004). Statistics of extremes, with applications in environment, insurance and finance. In B. Finkenstadt and H. Rootzen, editor, Extreme Values in Finance, Telecommunications and the Environment, pages 1–78. Chapman and Hall CRC Press, London.Google Scholar

Stein, M. L. (1999). Interpolation of Spatial Data. Springer-Verlag, New York. Some theory for Kriging.zbMATHGoogle Scholar

Wackernagel, H. (2003). Multivariate Geostatistics. An Introduction with Applications. Springer, Heidelberg, third edition.zbMATHGoogle Scholar