A New Estimator for a Tail Index

Acta Applicandae Mathematicae

Volumn 79, Issue 1-2, 2003, Pages 55-67

  Paulauskas, V ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Estimation; Tail index

Indexed keywords

COMPUTER SIMULATION; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

TAIL INDEX;

PROBABILITY DISTRIBUTIONS;

EID: 0142157220     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025818424104     Document Type: Conference Paper

References (19)

1. Breiman, L.: Probability, Addison-Wesley, Reading, Mass., 1968.
2. Beirlant, J., Teugels, J. L. and Vynckier, P.: Tail index estimation, Pareto quantile plots, and regression diagnostics, J. Amer. Statist. Assoc. 91 (1996), 1659-1667.
3. Csörgö, S., Deheuvels, P. and Mason, D.: Kernel estimates of the tail index of a distribution, Ann. Statist. 13 (1985), 1050-1077.
4. Danielsson, J., de Haan, L., Peng, L. and de Vries, C. G.: Using a bootstrap method to choose the sample fraction in tail index estimation, J. Multivariate Anal. 76 (2001), 226-248.
5. Davydov, Yu., Paulauskas, V. and Račkauskas, A.: More on P-stable convex sets in Banach spaces, J. Theoret. Probab. 13(1) (2000), 39-64.
6. Davydov, Yu. and Paulauskas, V.: On the estimation of the parameters of multivariate stable distributions, Acta Appl. Math. 58 (1999), 107-124.
7. de Haan, L. and Peng, L.: Comparison of tail index estimators, Statist. Nederlandica 52(1) (1998), 60-70.
8. de Haan, L. and Resnick, S.: Method to choose the sample fraction in tail index estimation, J. Roy. Statitst. Soc. Ser. B 42 (1980), 83-87.
9. Dekkers, A. L. M., Einmahl, J. H. J. and de Haan, L.: A moment estimator for the index of an extreme-value distribution, Ann. Statist. 17 (1975), 1833-1855.
10. Dekkers, A. L. M. and de Haan, L.: Optimal choice of sample fraction in extreme-value estimation, J. Multivariate Anal. 47(2) (1993), 172-173.
11. Draisma, G., de Haan, L. and Peng, L.: A Bootstrap-based method to achieve optimality in estimating the extreme-value index, Extremes 2(4) (1999), 367-404.
12. Drees, H., de Haan, L. and Resnick, S.: How to make a Hill plot, Ann. Statist. 28(1) (2000), 254-274.
13. Drees, H. and Kaufmann, E.: Selecting the optimal sample fraction in univariate extreme value estimation, Stochastic Process. Appl. 75(2) (1998), 149-172.
14. Hall, P.: Using the bootstrap to estimate means squared error and select smoothing parameter in nonparametric problems, J. Multivariate Anal. 32 (1990), 177-203.
15. Hill, B. M.: A simple general approach to inference about the tail of a distribution, Ann. Statist. 3 (1975), 1163-1174.
16. Geluk, J. L. and Peng, L.: An adaptive optimal estimate of the tail index for MA(1) time series, Statist. Probab. Lett. 46 (2000), 217-227.
17. Korn, G. A. and Korn, T. M.: Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York, 1961.
18. Paulauskas, V: A new estimator for tail index, Preprint, Vilnius University, 2002.
19. Pickands, J.: Statistical inference using extreme order statistics, Ann. Statist. 3(1) (1975), 119-131.