Existence and consistency of the maximum likelihood estimator for the extreme value index

Journal of Multivariate Analysis

Volumn 100, Issue 4, 2009, Pages 794-815

  Zhou, Chen ^a  

^a DE NEDERLANDSCHE BANK   (Netherlands)

Author keywords

62G05; Consistency; Extreme value condition; Extreme value index; Maximum likelihood estimator

Indexed keywords

EID: 58349122872     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2008.08.009     Document Type: Article

References (16)

1. Gnedenko B. Sur la distribution limite du terme maximum d'une série aléatoire. Ann. of Math. 44 (1943) 423-453
2. de Haan L. Slow variation and characterization of domains of attraction. In: Tiago de Oliveira J. (Ed). Statistical Extremes and Application (1984), Reidel Publishing 31-38
3. Hill B. A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 (1975) 1163-1174
4. Pickands III J. Statistical inference using extreme order statistics. Ann. Statist. 3 (1975) 119-131
5. Dekkers A., Einmahl J., and de Haan L. A moment estimator for the index of an extreme-value distribution. Ann. Statist. 17 (1989) 1833-1855
6. Balkema A., and de Haan L. Residual life time at great age. Ann. Probab. 2 (1974) 792-804
7. Smith R. Estimating tails of probability distributions. Ann. Statist. 15 (1987) 1174-1207
8. Drees H., Ferreira A., and de Haan L. On maximum likelihood estimation of the extreme value index. Ann. Appl. Probab. 14 (2004) 1179-1201
9. Grimshaw S. Computing maximum likelihood estimates for the generalized pareto distribution. Technometrics 35 (1993) 185-191
10. de Haan L., and Stadtmüller U. Generalized regular variation of second order. J. Austrl. Math. Soc. Ser. A 61 (1996) 381-395
11. Deheuvels P., Haeusler E., and Mason D. Almost sure convergence of the Hill estimator. Math. Proc. Cambridge. Philos. Soc. 104 (1988) 371-381
12. Einmahl J., and Mason D. Strong limit theorems for weighted quantile processes. Ann. Probab. 16 (1988) 1623-1643
13. J. Geluk, L. de Haan, Regular variation, extensions and Tauberian theorems. CWI Tract 40, Center for Mathematics and Computer Science, Amsterdam, Netherlands, 1987
14. de Haan L., and Ferreira A. Extreme Value Theory: An Introduction (2006), Springer
15. Falk M. Some best parameter estimates for distributions with finite endpoint. Statistics 27 (1995) 115-125
16. Shorack G., and Wellner J. Empirical Processes with Applications to Statistics (1986), John Wiley & Sons, Inc