A general class of estimators of the extreme value index

Journal of Statistical Planning and Inference

Volumn 66, Issue 1, 1998, Pages 95-112

  Drees, Holger ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Adaptive estimator; Empirical tail quantile function; Extreme value distribution; Extreme value index; Hadamard differentiability; Location invariance; Statistical tail functional

Indexed keywords

EID: 0032484340     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(97)00076-1     Document Type: Article

References (23)

1. Csörgo, S., Deheuvels, P., Mason, D., 1985. Kernel estimates of the tail index of a distribution. Ann. Statist. 13, 1050-1077.
2. Davis, R.A., Resnick, S., 1984. Tail estimates motivated by extreme value theory. Ann. Statist. 12, 1467-1487.
3. Dekkers, A.L.M., Einmahl, J.H.J., de Haan, L., 1989. A moment estimator for the index of an extreme value distribution. Ann. Statist. 17, 1833-1855.
4. Dekkers, A.L.M., de Haan, L., 1989. On the estimation of the extreme-value index and large quantile estimation. Ann. Statist. 17, 1795-1832.
5. Dekkers, A.L.M., de Haan, L., 1993. Optimal choice of sample fraction in extreme value estimation. J. Multivariate Anal. 47, 173-195.
6. Drees, H., 1995a. Refined Pickands estimators of the extreme value index. Ann. Statist. 23, 2059-2080.
7. Drees, H., 1995b. On smooth statistical tail functionals. Preprint, submitted.
8. Drees, H., 1996. Refined Pickands estimators with bias correction. Commun. Statist. Theory Methods 25, 837-852.
9. Einmahl, J.H.J., 1992. Limit theorems for tail processes with application to intermediate quantile estimation. J. Statist. Planning Infer. 32, 137-145.
10. Fernholz, L.T., 1983. Von Mises Calculus for Statistical Functionals. Lecture Notes in Statistics, vol. 19, Springer, New York.
11. Galambos, J., 1978. The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.
12. Gnedenko, B., 1943. Sur la distribution limit du terme maximum d'une série aléatoire. Ann. Math. 44, 423-453.
13. Haan, L. de, 1984. Slow variation and characterization of domains of attraction. In: Tiago de Oliveira, J., (Ed.), Statistical Extremes and Applications. Reidel Publishing, Dordrecht, pp. 31-38.
14. Haan, L. de, Rootzén, H., 1993. On the estimation of high quantiles. J. Statist. Plann. Infer. 35, 1-13.
15. Haan, L. de, Stadtmüller, U., 1996. Generalized regular variation of second order. J. Austr. Math. Soc., 61, 381-395.
16. Haeusler, E., Teugels, J.L., 1985. On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann. Statist. 13, 743-756.
17. Hall, P., 1982. On some simple estimates of an exponent of regular variation. J. Roy. Statist. Soc. Ser. B 44, 37-42.
18. Hall, P., Welsh, A.H., 1984. Best attainable rates of convergence for estimates of parameters of regular variation. Ann. Statist. 12, 1079-1084.
19. Hall, P., Welsh, A.H., 1985. Adaptive estimates of parameters of regular variation. Ann. Statist. 13, 331-341.
20. Hill, B.M., 1975. A simple general approach to inference about the tail of a distribution. Ann. Statist. 3, 1163-1174.
21. Pickands III, J., 1975. Statistical inference using extreme order statistics. Ann. Statist. 3, 119-131.
22. Reiss, R.-D., 1989. Approximate Distributions of Order Statistics, Springer Series in Statistics. Springer, New York.
23. Smith, R.L., 1987. Estimating tails of probability distributions. Ann. Statist. 15, 1174-1207.