References
- Paulauskas V, Vaičiulis M. Several new tail index estimators. To appear in Ann Inst Stat Math. http://dx.doi.org/10.1007/s10463-015-0548-3.
- Hill BM. A simple general approach to inference about the tail of a distribution. Ann Statist. 1975;3:1163–1174. doi: 10.1214/aos/1176343247
- Paulauskas V, Vaičiulis M. On the improvement of Hill and some others estimators. Lith Math J. 2013;53:336–355. doi: 10.1007/s10986-013-9212-x
- Beran J, Schell D, Stehlik M. The harmonic moment tail index estimator: asymptotic distribution and robustness. Ann Inst Statist Math. 2014;66:193–220. doi: 10.1007/s10463-013-0412-2
- Brilhante MF, Gomes MI, Pestana D. A simple generalization of the Hill estimator. Comput Stat Data Anal. 2013;57:518–535. doi: 10.1016/j.csda.2012.07.019
- Danielsson J, Jansen DW, de Vries CG. The method of moments ratio estimator for the tail shape parameter. Commun Stat Theory. 1996;25:711–720. doi: 10.1080/03610929608831727
- Gomes MI, Martins MJ. Efficient alternatives to the Hill estimator. In: Proceedings of the Workshop V.E.L.A. Extreme Values and Additive Laws, C.E.A.U.L. editions; 1999. p. 40–43.
- Gomes MI, Martins MJ, Neves M. Alternatives to a semiparametric estimation of parameters of rare events – the Jacknife methodology. Extremes. 2000;3:207–229. doi: 10.1023/A:1011470010228
- Gomes MI, Martins MJ. Generalizations of the Hill estimator – asymptotic versus finite sample behaviour. J Stat Plan Infer. 2001;93:161–180. doi: 10.1016/S0378-3758(00)00201-9
- Caeiro F, Gomes MI. A class of asymptotically unbiased semi-parametric estimators of the tail index. Test. 2002;11:345–364. doi: 10.1007/BF02595711
- De Haan L, Peng L. Comparison of tail index estimators. Stat Neerlandica. 1998;52:60–70. doi: 10.1111/1467-9574.00068
- De Haan L, Ferreira A. Extreme value theory: an introduction. New York: Springer; 2006. Chapter 2, Extreme and Intermediate Order Statistics; p. 37–64.
- Dekkers ALM, de Haan L. Optimal choice of sample fraction in extreme-value estimation. J Multivariate Anal. 1993;47:173–195. doi: 10.1006/jmva.1993.1078
- Corless RM, Gonner GH, Hare DE, et al. On the Lambert W Function. Adv Comput Math. 1996;5:329–359. doi: 10.1007/BF02124750
- Gomes MI, Henriques-Rodrigues L. Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation? Discuss Math Probab Stat. 2010;30:35–51. doi: 10.7151/dmps.1120
- Hall P. On some simple estimates of an exponent of regular variation. J R Statist Soc Ser B. 1982;44:37–42.
- Hall P, Welsh AH. Adaptive estimates of parameters of regular variation. Ann Statist. 1985;13:331–341. doi: 10.1214/aos/1176346596
- Drees H. A general class of estimators of the extreme value index. J Stat Plan Infer. 1998;66:95–112. doi: 10.1016/S0378-3758(97)00076-1
- Fraga Alves MI, Gomes MI, de Haan L. A new class of semi-parametric estimators of the second order parameter. Portugaliae Math. 2003;60:193–214.
- Gomes MI, Pestana D, Caeiro F. A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator. Stat Probab Lett. 2009;79:295–303. doi: 10.1016/j.spl.2008.08.016
- Gomes MI, Martins MJ. Asymptotically unbiased estimators of the tail index based on external estimation of the second order parameter. Extremes. 2002;5:5–31. doi: 10.1023/A:1020925908039
- Caeiro F, Gomes MI, Pestana D. Direct reduction of bias of the classical Hill estimator. Revstat. 2005;3:113–136.
- McElroy T, Politis DN. Moment-based tail index estimation. J Stat Plan Infer. 2007;137:1389–1406. doi: 10.1016/j.jspi.2006.04.002