Location invariant Weiss-Hill estimator

Araújo Santos, P., Fraga Alves, M.I., Gomes, M.I.: Peaks over random threshold methodology for tail index and quantile estimation. Revstat 4, 227–247 (2006)

Beirlant, J., Vynckier, P., Teugels, J.L.: Excess functions and estimation of the extreme-value index. Bernoulli 2, 293–318 (1996)

Caeiro, F., Gomes, M.I., Pestana, D.D. Direct reduction of bias of the classical Hill estimator. Revstat 3, 113–136 (2005)

de Haan, L.: Extreme value statistics. In: Galambos, J., Lechner, J., Simiu, E. (eds.) Extreme Value Theory and Applications, pp. 93–122. Kluwer Academic Publications, Dordrecht (1994)

de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction. Springer, New York (2006)

de Haan, L., Peng, L.: Comparison of tail index estimators. Stat. Neerl. 52, 60–70 (1998)

Dekkers, A.L.M., de Haan, L.: On the estimation the extreme-value index and large quantile estimation. Ann. Stat. 17, 1795–1832 (1989)

Dekkers, A.L.M., Einmahl, J.H.J., de Haan, L.: A moment estimator for the index of an extreme-value distribution. Ann. Stat. 17, 1833–1855 (1989)

Draisma, G., de Haan, L., Peng, L., Pereira, T.T.: A bootstrap-based method to achieve optimality in estimating the extreme-value index. Extremes 4, 367–404 (1999)

Falk, M.: Some best parameter estimates for distributions with finite endpoint. Statistics 27, 115–125 (1995)

Fraga Alves, M.I.: A location invariant Hill-type estimator. Extremes 4, 199–217 (2001a)

Fraga Alves, M.I.: Weiss-Hill estimator. Test 10, 203–224 (2001b)

Fraga Alves, M.I., Gomes M.I., de Haan, L., Neves, C.: Mixed moment estimators and location invariant alternatives. Extremes 12, 149–185 (2009)

Gomes, M.I., Henriques Rodrigues, L.: Tail index estimation for heavy tails: accommodation of bias in the excesses over a high threshold. Extremes 11, 303–328 (2008)

Gomes, M.I., Martins, M.J.: “Asymptotically unbiased” estimators of the tail index based on external estimation of the second order parameter. Extremes 5, 5–31 (2002)

Gomes, M.I., Martins, M.J.: Bias reduction and explicit estimation of the tail index. J. Stat. Plan. Inference 124, 361–378 (2004)

Gomes, M.I., Pestana, D.: A sturdy reduced bias extreme quantile (VaR) estimator. J. Am. Stat. Assoc. 102, 280–292 (2007)

Gomes, M.I, de Haan, L., Henriques Rodrigues, L.: Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses. J. R. Stat. Soc., Ser. B 70, 31–53 (2008a)

Gomes, M.I., Fraga Alves, M.I., Araújo Santos, P.: PORT Hill and moment estimators for heavy-tailed models. Commun. Stat., Simul. Comput. 37, 1281–1306 (2008b)

He, L.: Convergence of a kind of Pickands-type estimator. Acta Math. Sin., Chinese Series 47, 805–810 (2004)

Hill, B.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)

Li, J., Peng, Z., Nadarajah, S.: A class of unbiased location invariant Hill-type estimators for heavy tailed distributions. Electronic Journal of Statistics 2, 829–847 (2008)

Li, J., Peng, Z., Nadarajah, S.: Asymptotic normality of location invariant heavy tail index estimator. Extremes 13, 269–290 (2010)

Ling, C., Peng, Z., Nadarajah, S.: A location invariant Moment-type estimator I. Theory Probab. Math. Stat. 76, 23–31 (2007a)

Ling, C., Peng, Z., Nadarajah, S.: A location invariant Moment-type estimator II. Theory Probab. Math. Stat. 77, 177–189 (2007b)

Ling, C., Peng, Z., Nadarajah, S.: Selecting the optimal sample fraction in location invariant moment-type estimators. Theory Probab. Appl. (2009, in press)

Müller, S., Hüsler, J.: Iterative estimation of the extreme value index. Methodology and Computing in Applied Probability 2, 139–145 (2005)

Peng, Z.: Extension of Pickands’ estimator. Acta Math. Appl. Sin., Chinese Series 40, 759–762 (1997)

Peng, L.: Asymptotically unbiased estimator for the extreme-value index. Statistics and Probability Letters 2, 107–115 (1998a)

Peng, Z.: A kind of simplified Pickands-type estimator. Acta Math. Appl. Sin., Chinese Series 4, 539–542 (1998b)

Peng, L., Qi, Y.: A new calibration method of constructing empirical likelihood-based confidence intervals for the tail index. Aust. N. Z. J. Stat. 48, 59–66 (2006a)

Peng, L., Qi, Y.: Confidence regions for high quantiles of a heavy tailed distribution. Ann. Stat. 4, 1964–1986 (2006b)

Peng, Z., Nadarajah, S.: The Pickands’ estimator of the negative extreme value index. Acta Scientiarum Naturalium Universitatis Pekinensis 37, 12–19 (2001)

Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975)

Qi, Y.: On the tail index of a heavy tailed distribution. Ann. Inst. Stat. Math. 62, 277–298 (2010)

Segers, J.: Generalized Pickands estimators for the extreme value index. J. Stat. Plan. Inference 128, 381–396 (2005)

Weiss, L.: Asymptotic inference about a density function at the end of its range. Nav. Res. Logist. Q. 1, 111–114 (1971)