Estimation of the extreme value index and extreme quantiles under random censoring

Extremes

Volumn 10, Issue 3, 2007, Pages 151-174

  Beirlant, Jan ^a   Guillou, Armelle ^b   Dierckx, Goedele ^a   Fils Villetard, Amélie ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

Censoring; Extreme quantile; Extreme value index; Kaplan Meier estimator

Indexed keywords

EID: 36549054746     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-007-0039-x     Document Type: Article

References (20)

1. Andersen, P.K., Borgan, O., Gill, R.D., Keiding, N.: Statistical Models Based on Counting Processes. Springer, New York (1993)
2. Balkema, A., de Haan, L.: Residual life time at great age. Ann. Probab. 2, 792-804 (1974)
3. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes: Theory and Applications. Wiley, New York (2004)
4. Beirlant, J., Guillou, A.: Pareto index estimation under moderate right censoring. Scand. Actuar. J. 2, 111-125 (2001)
5. Beirlant, J., Vynckier, P., Teugels, J.L.: Excess functions and estimation of the extreme value index. Bernoulli 2, 293-318 (1996)
6. Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge Univ. Press, Cambridge, UK (1987)
7. Cox, D.R., Oakes, D.: Analysis of Survival Data. Chapman and Hall, New York (1984)
8. Csörgo, S.: Universal Gaussian approximations under random censorship. Ann. Stat. 24, 2744-2778 (1996)
9. Davison, A.G., Smith, R.L.: Models for exceedances over high thresholds. J. R. Stat. Soc., B 52(3), 393-442 (1990)
10. de Haan, L., Rootzén, H.: On the estimation of high quantiles. J. Stat. Plan. Inference 35, 1-13 (1993)
11. 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)
12. Draisma, G., de Haan, L., Peng, L., Pereira, T.T.: A bootstrap-based method to achieve optimality in estimating the extreme-value index. Extremes 2, 367-404 (1999)
13. Fils-Villetard, A.: Analyse des valeurs extrêmes et applications dans un cadre univarié et multivarié, Thèse de Doctorat, Paris 6 (2006)
14. Hall, P.: On some simple estimates of an exponent of regular variation. J. R. Stat. Soc., B 44, 37-42 (1982)
15. Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163-1174 (1975)
16. Hosmer, D.W., Lemeshow, S.: Applied Survival Analysis. Wiley, New York (1999)
17. Kaplan, E.L., Meier, P.: Non-parametric estimation from incomplete observations. J. Amer. Stat. Assoc. 53, 457-481 (1958)
18. Pickands III, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119-131 (1975)
19. Reiss, R.D., Thomas, M.: Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. Birkhäuser, Basel (1997)
20. Smith, R.L.: Estimating tails of probability distributions. Ann. Stat. 15, 1174-1207 (1987)