159
Views
6
CrossRef citations to date
0
Altmetric
Articles

A location-invariant probability weighted moment estimation of the Extreme Value Index

, &
Pages 676-695 | Received 13 Oct 2013, Accepted 26 Sep 2014, Published online: 06 Nov 2014

References

  • P. Araújo Santos, M.I. Fraga Alves, and M.I. Gomes, Peaks over random threshold methodology for tail index and quantile estimation, Revstat 4(3) (2006), pp. 227–247.
  • J. Beirlant, F. Caeiro, and M.I. Gomes, An overview and open research topics in the field of statistics of univariate extremes, Revstat 10(1) (2012), pp. 1–31.
  • M.F. Brilhante, M.I. Gomes, and D. Pestana, A simple generalization of the Hill estimator, Comput Statist. Data Anal. 57(1) (2013), pp. 518–535. doi: 10.1016/j.csda.2012.07.019
  • F. Caeiro and M.I. Gomes, Semi-parametric tail inference through probability-weighted moments, J. Statist. Plan. Inference 141(2) (2011), pp. 937–950. doi: 10.1016/j.jspi.2010.08.015
  • F. Caeiro, M.I. Gomes, and D.D. Pestana, Direct reduction of bias of the classical Hill estimator, Revstat 3(2) (2005), pp. 111–136.
  • F. Caeiro, M.I. Gomes, and L. Henriques-Rodrigues, Reduced-bias tail index estimators under a third order framework, Commun. Statist. – Theory Methods 38(7) (2009), pp. 1019–1040. doi: 10.1080/03610920802361415
  • F. Caeiro, M.I. Gomes, and L. Henriques-Rodrigues, (2013). A Location Invariant Probability Weighted EVI-Estimator. Notas e Comunicações CEAUL 30/2013. Available at http://www.ceaul.fc.ul.pt/notas.html?ano=2013.
  • F. Caeiro, M.I. Gomes, and B. Vandewalle, Semi-parametric probability-weighted moments estimation revisited, Methodol. Comput. Appl. Probab. 16(1) (2014), pp. 1–29. doi: 10.1007/s11009-012-9295-6
  • A.L.M. Dekkers and L. de Haan, Optimal choice of sample fraction in extreme-value estimation, J. Multivariate Anal. 47 (1993), pp. 173–195. doi: 10.1006/jmva.1993.1078
  • M.I. Fraga Alves, M.I. Gomes, and L. de Haan, A new class of semi-parametric estimators of the second order parameter, Port. Math. 60(2) (2003), pp. 194–213.
  • M.I. Fraga Alves, M.I. Gomes, L. de Haan, and C. Neves, Mixed moment estimators and location invariant alternatives, Extremes 12 (2009), pp. 149–185. doi: 10.1007/s10687-008-0073-3
  • J. Geluk and L. de Haan, Regular Variation, Extensions and Tauberian Theorems. Tech. Report CWI Tract 40, Centre for Mathematics and Computer Science, Amsterdam, Netherlands, 1987.
  • B.V. Gnedenko, Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math. 44 (1943), pp. 423–453. doi: 10.2307/1968974
  • M.I. Gomes and A. Guillou, Extreme value theory and statistics of univariate extremes: A review, Int. Statist. Rev. (2014). doi:10.1111/insr.12058.
  • M.I. Gomes and M.J. Martins, ‘Asymptotically unbiased’ estimators of the tail index based on external estimation of the second order parameter, Extremes 5(1) (2002), pp. 5–31. doi: 10.1023/A:1020925908039
  • M.I. Gomes and O. Oliveira, The bootstrap methodology in Statistics of Extremes: Choice of the optimal sample fraction, Extremes 4(4) (2001), pp. 331–358. doi: 10.1023/A:1016592028871
  • M.I. Gomes and D. Pestana, A simple second order reduced-bias' tail index estimator, J. Statist. Comput. Simul. 77(6) (2007), pp. 487–504. doi: 10.1080/10629360500282239
  • M.I. Gomes, M.I. Fraga Alves, and P. Araújo Santos, PORT Hill and Moment Estimators for Heavy-Tailed Models, Commun. Statist. – Simul. Comput. 37 (2008), pp. 1281–1306. doi: 10.1080/03610910802050910
  • M.I. Gomes, L. de Haan, and L. Henriques-Rodrigues, Tail Index estimation for heavy-tailed models: Accommodation of bias in weighted log-excesses, J. R. Statist. Soc. B70(1) (2008), pp. 31–52.
  • M.I. Gomes, F. Caeiro, and L. Henriques-Rodrigues, PORT-PPWM extreme value index estimation, in Proceedings of COMPSTAT, A. Colubi, K. Fokianos, E.J. Kontoghiorghes and G. González-Rodríguez, eds., The International Statistical Institute/International Association for Statistical Computing, Limassol, Cyprus, 2012, pp. 259–270.
  • M.I. Gomes, F. Figueiredo, and M.M. Neves, Adaptive estimation of heavy right tails: The bootstrap methodology in action, Extremes 15 (2012), pp. 463–489. doi: 10.1007/s10687-011-0146-6
  • M.I. Gomes, L. Henriques-Rodrigues, M.I. Fraga Alves, and B.G. Manjunath, Adaptive PORT-MVRB estimation: An empirical comparison of two heuristic algorithms, J. Statist. Comput. Simul. 83(6) (2013), pp. 1129–1144. doi: 10.1080/00949655.2011.652113
  • L de Haan, Slow variation and characterization of domains of attraction, in Statistical Extremes and Applications, T. de Oliveira, ed., D. Reidel, Dordrecht, 1984, pp. 31–48.
  • L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction, Springer Science+Business Media, LLC, New York, 2006.
  • L. de Haan and L. Peng, Comparison of tail index estimators, Statist. Neerlandica 52 (1998), pp. 60–70. doi: 10.1111/1467-9574.00068
  • B.M. Hill, A simple general approach to inference about the tail of a distribution, Ann. Statist. 3(5) (1975), pp. 1163–1174. doi: 10.1214/aos/1176343247
  • C. Scarrot and A. McDonald, A review of extreme value threshold estimation and uncertainty quantification, Revstat 10(2) (2012), pp. 33–60.

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.