Abstract
In Chapters 3 to 7 we focused on representations and modeling techniques for extremes of a single process. We now turn attention to multivariate extremes. When studying the extremes of two or more processes, each individual process can be modeled using univariate techniques, but there are strong arguments for also studying the extreme value inter-relationships. First, it may be that some combination of the processes is of greater interest than the individual processes themselves; second, in a multivariate model, there is the potential for data on each variable to inform inferences on each of the others. Examples 1.9–1.11 illustrate situations where such techniques may be applicable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Further Reading
Barnett, V. (1976). The ordering of multivariate data (with discussion). Journal of the Royal Statistical Society, A 139, 318–355.
De Haan, L. and Resnick, S. I. (1977). Limit theory for multivariate sample extremes. Zeit. Wahrscheinl.-theorie 40, 317–337.
Pickands, J. (1981). Multivariate extreme value distributions. In Proceedings of the 43rd Session of the I.S.I., pages 859–878, The Hague. International Statistical Institute.
Resnick, S. I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer Verlag, New York.
Davison, A. C. (1984). Modelling excesses over high thresholds, with an application. In Tiago de Oliveira, J., editor, Statistical Extremes and Applications, pages 461–482. Reidel, Dordrecht.
Buishand, T. A. (1991). Extreme rainfall estimation by combining data from several sites. Hydrological Science Journal 36, 345–365.
Buishand, T. A. (1984). Bivariate extreme value data and the station-year method. Journal of Hydrology 69, 77–95.
Tawn, J. A. (1988a). Bivariate extreme value theory: models and estimation. Biometrika 75, 397–415.
Coles, S. G. and Walshaw, D. (1994). Directional modelling of extreme wind speeds. Applied Statistics 43, 139–157.
Coles, S. G. and Tawn, J. A. (1991). Modelling extreme multivariate events. Journal of the Royal Statistical Society, B 53, 377–392.
Joe, H., Smith, R. L., and Weissman, I. (1992). Bivariate threshold methods for extremes. Journal of the Royal Statistical Society, B 54, 171–183.
Joe, H. (1989). Families of min-stable multivariate exponential and multivariate extreme value distributions. Statistics and Probability Letters 9, 75–81.
Joe, H. (1994). Multivariate extreme value distributions with applications to environmental data. Canadian Journal of Statistics 22, 47–64.
Coles, S. G. and Tawn, J. A. (1990). Statistics of coastal flood prevention. Philosophical Transactions of the Royal Society of London, A 332, 457476.
Coles, S. G., Tawn, J. A., and Smith, R. L. (1994). A seasonal Markov model for extremely low temperatures. Environmetrics 5, 221–239.
Tawn, J. A. (1994). Applications of multivariate extremes. In Galambos, J., Lechner, J., and Simiu, E., editors, Extreme Value Theory and Applications, pages 249–268. Kluwer, Dordrecht.
Ledford, A. and Tawn, J. A. (1998). Concomitant tail behaviour for extremes. Advances in Applied Probability 30, 197–215.
Hüsler, J. (1996). Multivariate option price models and extremes. Communications in Statistics: Theory and Methods 25, 853–870.
Hüsler, J. (1996). Multivariate option price models and extremes. Communications in Statistics: Theory and Methods 25, 853–870.
Deheuvels, P. and Tiago DE Oliveira, J. (1989). On the nonparametric estimation of the bivariate extreme value distributions. Statistics and Probability Letters 8, 315–323.
Hall, P. and Tajvidi, N. (2000a). Distribution and dependence function estimation for bivariate extreme value distributions. Bernoulli 6, 835844.
Sibuya, M. (1960). Bivariate extreme statistics. Ann. Inst. Statist. Math. 11, 195–210.
Ledford, A. and Tawn, J. A. (1997). Modelling dependence with in joint
Coles, S. G. and Casson, E. A. (1999). Spatial regression models for extremes. Extremes 1, 449–468.
Hsing, T. (1989). Extreme value theory for multivariate stationary sequences. Journal of Multivariate Analysis 29, 274–291.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag London
About this chapter
Cite this chapter
Coles, S. (2001). Multivariate Extremes. In: An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer, London. https://doi.org/10.1007/978-1-4471-3675-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3675-0_8
Publisher Name: Springer, London
Print ISBN: 978-1-84996-874-4
Online ISBN: 978-1-4471-3675-0
eBook Packages: Springer Book Archive