A new blocks estimator for the extremal index

References

• Cai, J. J. 2019. A nonparametric estimator of the extremal index. arXiv 1911.06674
   Google Scholar
• Chernick, M. R. 1978. Mixing conditions and limit theorems for maxima of some stationary sequences. PhD diss., Stanford University.
   Google Scholar
• Chernick, M. R., T. Hsing, and W. P. McCormick. 1991. Calculating the extremal index for a class of stationary sequences. Advances in Applied Probability 23 (4):835–50. doi:10.2307/1427679.
   Web of Science ®Google Scholar
• Davis, R., and S. Resnick. 1989. Basic properties and prediction of max-ARMA processes. Advances in Applied Probability 21 (4):781–803. doi:10.2307/1427767.
   Web of Science ®Google Scholar
• Deheuvels, P. 1983. Point processes and multivariate extreme values. Journal of Multivariate Analysis 13 (2):257–72. doi:10.1016/0047-259X(83)90025-8.
   Web of Science ®Google Scholar
• Embrechts, P., C. Klüppelberg, and T. Mikosch. 1997. Modelling extremal events. Berlin: Springer.
   Google Scholar
• Ferreira, H., and M. Ferreira. 2012a. On extremal dependence of block vectors. Kybernetika 48 (5):988–1006.
   Web of Science ®Google Scholar
• Ferreira, H., and M. Ferreira. 2012b. Fragility index of block tailed vectors. Journal of Statistical Planning and Inference 142 (7):1837–48. doi:10.1016/j.jspi.2012.01.021.
   Web of Science ®Google Scholar
• Ferreira, H., and M. Ferreira. 2018. Estimating the extremal index through local dependence. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 54 (2):587–605.
   Web of Science ®Google Scholar
• Ferreira, M. 2013. Nonparametric estimation of the tail-dependence coefficient. REVSTAT - Statistical Journal 11 (1):1–16.
   Web of Science ®Google Scholar
• Ferreira, M., and H. Ferreira. 2012c. On extremal dependence: Some contributions. TEST 21 (3):566–83. doi:10.1007/s11749-011-0261-3.
   Web of Science ®Google Scholar
• Ferro, C. A. T., and J. Segers. 2003. Inference for clusters of extreme values. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65 (2):545–56. doi:10.1111/1467-9868.00401.
   Web of Science ®Google Scholar
• Frahm, G., M. Junker, and R. Schmidt. 2005. Estimating the tail-dependence coefficient: Properties and pitfalls. Insurance: Mathematics & Economics 37 (1):80–100.
   Web of Science ®Google Scholar
• Gomes, D. P., and M. M. Neves. 2020. Extremal index blocks estimator: The threshold and the block size choice. Journal of Applied Statistics 47 (13-15):2846–61. doi:10.1080/02664763.2020.1720626.
   PubMed Web of Science ®Google Scholar
• Hsing, T., J. Hüsler, and M. R. Leadbetter. 1988. On the exceedance point process for a stationary sequence. Probability Theory and Related Fields 78 (1):97–112. doi:10.1007/BF00718038.
   Web of Science ®Google Scholar
• Huang, X. 1992. Statistics of bivariate extreme values. PhD thes., Erasmus University Rotterdam, Tinbergen, Institute Research Series 22.
   Google Scholar
• Martins, A. P., and H. Ferreira. 2014. Extremal properties of M4 processes. Test 23 (2):388–408. doi:10.1007/s11749-014-0358-6.
   Web of Science ®Google Scholar
• Moloney, N. R., D. Faranda, and Y. Sato. 2019. An overview of the extremal index. Chaos 29 (2):022101. doi:10.1063/1.5079656.
   PubMed Web of Science ®Google Scholar
• Northrop, P. J. 2015. An efficient semiparametric maxima estimator of the extremal index. Extremes 18 (4):585–603. doi:10.1007/s10687-015-0221-5.
   Web of Science ®Google Scholar
• Northrop, P. J., and C. Christodoulides. 2019. Exdex: Estimation of the Extremal Index. https://CRAN.R-project.org/package=exdex.
   Google Scholar
• Smith, R. 1992. The Extremal Index for a Markov chain. Journal of Applied Probability 29 (1):37–45. doi:10.2307/3214789.
   Web of Science ®Google Scholar
• Smith, R. L., and I. Weissman. 1996. Characterization and estimation of the multivariate extremal index. Manuscript, UNC.
   Google Scholar
• Stephenson, A. G. 2002. evd: Extreme value distributions. R News 2 (2):31–2. https://CRAN.R-project.org/doc/Rnews/.
   Google Scholar
• Süveges, M., and A. C. Davison. 2010. Model misspecification in peaks over threshold analysis. Annals of Applied Statistics 4:203–21.
   Web of Science ®Google Scholar
• Weissman, I., and S. Y. Novak. 1998. On blocks and runs estimators of the extremal index. Journal of Statistical Planning and Inference 66 (2):281–8. doi:10.1016/S0378-3758(97)00095-5.
   Web of Science ®Google Scholar