142
Views
2
CrossRef citations to date
0
Altmetric
Articles

A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications

, &
Pages 549-572 | Accepted 06 Nov 2013, Published online: 15 Jan 2014

References

  • Beirlant, J., Dierckx, G. & Guillou, A. (2005). Estimation of the extreme value index and regression on generalized quantile plots. Bernoulli 11, 949–970.
  • Beirlant, J., Goegebeur, Y., Segers, J. & Teugels, J. L. (2004). Statistics of extremes: theory and applications. Chichester: John Wiley & Sons.
  • Beirlant, J., Vynckier, P. & Teugels, J. L. (1996). Excess functions and estimation of the extreme value index. Bernoulli 2, 293–318.
  • Billingsley, P. (1999). Convergence of probability measures, 2nd ed. New York: Wiley-Interscience.
  • Cebrián, A. C., Denuit, M. & Lambert, M. (2003). Analysis of bivariate tail dependence using extreme value copulas: an application to the SOA medical large claims database. Belgian Actuarial Bulletin 3(1), 33–41.
  • Corcoran, J. N. & Schneider, U. (2003). Shift and scale coupling methods for perfect simulation. Probability in the Engineering and Informational Sciences 17, 277–303.
  • Davis, R. A. & Mikosch, T. (1998). The sample autocorrelation of heavy-tailed processes with applications to arch. Annals of Statistics 26, 2049–2080.
  • Dekkers, A. L. M., Einmahl, J. H. J. & de Haan, L. (1989). A moment estimator for the index of an extreme-value distribution. Annals of Statistics 17, 1833–1855.
  • Einmahl, J. H. J., de Haan, L. & Huang, X. (1993). Estimating a multidimensional extreme-value distribution. Journal of Multivariate Analysis 47, 35–47.
  • Einmahl, J. H. J., de Haan, L. & Piterbarg, V. I. (2001). Nonparametric estimation of the spectral measure of an extreme value distribution. Annals of Statistics 29, 1401–1423.
  • Einmahl, J. H. J., de Haan, L. & Sinha, A. K. (1997). Estimating the spectral measure of an extreme value distribution. Stochastic Processes and their Applications 70, 143–171.
  • Einmahl, J. H. J. & Segers, J. (2009). Maximum empirical likelihood estimation of the spectral measure of an extreme value distribution. Annals of Statistics 37, 2953–2989.
  • Embrechts, P., Klüppelberg, C. & Mikosch, T. (1997). Modelling extremal events for insurance and finance. Berlin: Springer-Verlag.
  • Engle, R. F. (1982). Autoregressive conditional heteroscedastic models with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.
  • Frees, E. W. & Valdez, E. A. (1998). Understanding using copulas. The North American Actuarial Journal 2, 1–25.
  • Gumbel, E. J. (1960). Distributions des valeurs extrêmes en plusieurs dimensions. Publications de l’Institut de Statistique de l’Université de Paris 9, 171–173.
  • de Haan, L. & Ferreira, A. (2006). Extreme value theory: an introduction. New York: Springer-Verlag.
  • de Haan, L. & Resnick, S. I. (1977). Limit theory for multivariate sample extremes. Zeitschrift für Warscheinlichkeitstheorie und Verwandte Gebiete 40, 317–337.
  • de Haan, L. & de Ronde, J. (1998). Sea and wind: multivariate extremes at work. Extremes 1, 7–46.
  • Hill, B. M. (1975). A simple general approach about the tail of a distribution. Annals of Statistics 3, 1163–1174.
  • Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics 3, 119–131.
  • Resnick, S. I. (1987). Extreme values, regular variation and point processes. New York: Springer-Verlag.
  • Resnick, S. I. (2006). Heavy-tail phenomena: probabilistic and statistical modeling. New York: Springer-Verlag.
  • Tawn, J. A. (1988). Bivariate extreme value theory: models and estimation. Biometrika 75, 397–415.
  • Weissman, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. Journal of the American Statistical Association 73, 812–815.
  • You, A., Schneider, U., Guillou, A. & Naveau, P. (2010). Improving extreme quantile estimation via a folding procedure. Journal of Statistical Planning and Inference 140, 1775–1787.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.