Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution

Annals of Statistics

Volumn 37, Issue 5 B, 2009, Pages 2953-2989

  Einmahl, John H J ^a   Segers, Johan ^b  

^a TILBURG UNIVERSITY   (Netherlands)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Functional central limit theorem; Local empirical process; Moment constraint; Multivariate extremes; National Health and Nutrition Examination Survey; Nonparametric maximum likelihood estimator; Tail dependence

Indexed keywords

EID: 69049112909     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS677     Document Type: Article

References (25)

1. Abdous, B. and Ghoudi, K. (2005). Nonparametric estimators of multivariate extremedependence functions. J. Nonparametr. Statist. 17 915-935. MR2192166
2. eirlant, J., Goegebeur, Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications. Wiley, Chichester. MR2108013
3. aperaA, P. and Fougeres, A.-L. (2000). Estimation of a bivariate extreme-value distribution. Extremes 3 311-329. MR1870461
4. Coles, S. (2001). An Introduction to Statistical Modelling of Extreme Values. Springer, New York. MR1932132
5. Coles, S. and Tawn, J. (1991). Modelling extreme-multivariate events. J. Roy. Statist. Soc. Ser. B 53 377-392. MR1108334
6. Cs6rgO, M. and Horvath, L. (1993). Weighted Approximations in Probability and Statistics. Wiley, Chichester. MR1215046
7. rees, H. and Huang, X. (1998). Best attainable rates of convergence for estimates of the stable ail dependence function. J. Multivariate Anal. 64 25-47. MR1619974
8. Einmahl, J. (1997). Poisson and Gaussian approximation of weighted local empirical processes. tochastic Process. Appl. 70 31-58. MR1472958
9. Einmahl, J., de Haan, L. and Li, D. (2006). Weighted approximations of tail copula processes with application to testing the bivariate extreme-value condition. Ann. Statist. 34 1987-2014. MR2283724
10. Einmahl, J., de Haan, L. and Piterbarg, V. (2001). Nonparametric estimation of the spectral measure of an extreme-value distribution. Ann. Statist. 29 1401-1423. MR1873336
11. Einmahl, J., de Haan, L. and Sinha, A. (1997). Estimating the spectral measure of an extremevalue distribution. Stochastic Process. Appl. 70 143-171. MR1475660
12. Einmahl, J., Krajina, A. and Segers, J. (2008). A method of moments estimator for tail depenence. Bernoulli 14 1003-1026.
13. Frees, E.W. and Valdez, E. A. (1998). Understanding relationships using copulas. N. Am. Actuar. J. 2 1-25. MR1988432
14. Genest, C., Ghoudi, K. and Rivest, L.-P. (1998). Discussion of Frees and Valdez (1998). N.Am. Actuar. J. 2 143-149. MR2011244
15. Gumbel, E. J. (I960). Bivariate exponential distributions. J. Amer. Statist. Assoc. 55 698-707. MR0116403
16. de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer, New York. MR2234156
17. De Haan, L., Neves, C. and Peng, L. (2008). Parametric tail copula estimation and model testing. J. Multivariate Anal. 99 1260-1275. MR2419346
18. de Haan, L. and Resnick, S. (1977). Limit theory for multidimensional sample extremes. Wahrsch. Verw. Gebiete 40 317-337. MR0478290
19. Huang, X. (1992). Statistics of Bivariate Extremes. Ph.D. thesis, Erasmus Univ. Rotterdam.
20. Joe, H., Smith, R.L. and Weissman, I. (1992). Bivariate threshold methods for extremes. J. Roy. Statist. Soc. Ser. B 54 171-183. MR1157718
21. Ledford, A. W. and Tawn, J. A. (1996). Statistics for near independence in multivariate extreme values. Biometrika 83 169-187. MR1399163
22. National Center for Health Statistics (2007). National Health and Nutrition Examination Survey 2005-2006. Available at http://www.cdc.gov/nchs/ about/major/nhanes/nhanes2005-2006/exam05-06.htm.
23. Owen, A. (2001). Empirical Likelihood. Chapman & Hall/CRC, Boca Raton, FL.
24. Pickands, J. (1981). Multivariate extreme-value distributions. In Proceedings of the 43rd session of the International Statistical Institute, Vol.2 (Buenos Aires, 1981) 49 859-878, 894-902. With a discussion. MR0820979
25. Tawn, J. A. (1988). Bivariate extreme-value theory: Models and estimation. Biometrika 75 397-415. MR0967580