Estimating the index of a stable law via the pot-method

Statistics and Probability Letters

Volumn 41, Issue 2, 1999, Pages 413-423

  Marohn, Frank ^a  

^a CATHOLIC UNIVERSITY OF EICHSTÄTT INGOLSTADT   (Germany)

Author keywords

Asymptotic efficiency; Central sequence; Finite sample size properties; Generalized Pareto distribution; Hill estimator; LAN; Peaks over threshold; Point process of exceedances; Stable distribution

Indexed keywords

EID: 0043229476     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(98)00210-7     Document Type: Article

References (26)

1. Chambers, J.M., Mallows, C.L., Stuck, B.W., 1976. A method for simulating stable random variables. J. Amer. Statist. Assoc. 71, 340-344.
2. DeHaan, L., Resnick, S.I., 1980. A simple asymptotic estimate for the index of a stable distribution. J. Roy. Statist. Soc. Ser. B 42, 83-87.
3. DuMouchel, W.H., 1973. On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution. Ann. Statist. 1, 948-957.
4. DuMouchel, W.H., 1983. Estimating the stable index α in order to measure tail thickness: A critique. Ann. Statist. 11, 1019-1031.
5. Falk, M., 1995. On testing the extreme value index via the POT-method. Ann. Statist. 23, 2013-2035.
6. Falk, M., 1998. Local asymptotic normality of truncated empirical processes. Ann. Statist. 26, 697-718.
7. Falk, M., Marohn, F., 1997. Efficient estimation of the shape parameter in Pareto models with partially known scale. Statist. Decisions 15, 229-239.
8. Falk, M., Hüsler, J., Reiss, R.-D., 1994. Laws of Small Numbers: Extremes and Rare Events. Birkhäuser, Basel.
9. Feller, W.F., 1971. An Introduction to Probability Theory and Its Applications, 2nd Ed., vol. II. Wiley, New York.
10. Hall, P., 1982. On some simple estimates of an exponent of regular variation. J. Roy. Statist. Soc. Ser. B 44, 37-42.
11. Hill, B.M., 1975. A simple approach to inference about the tail of a distribution. Ann. Statist. 13, 331-341.
12. Höpfner, R., 1997a. On tail parameter estimation in certain point process models. J. Statist. Planning and Inference 60, 169-187.
13. Höpfner, R., 1997b. Two comments in parameter estimation in stable processes. Math. Meth. Statist. 6, 125-134.
14. Höpfner, R., 1998. Estimating a stability parameter: Asymptotics and simulations. Statistics 30, 291-305.
15. Höpfner, R., Jacod, J., 1994. Some remarks on the joint estimation of the index and the scale parameter for stable processes. In: Mandl, P., Huskova, M. (Eds.), Asymptotic Statistics, Proc. 5th Prague Symp. Physica, Heidelberg, pp. 273-284.
16. Höpfner, R., Rüschendorf, L., 1996. Comparison of Estimators in Stable Models. Preprint Universität Freiburg.
17. Kaufmann, E., Reiss, R.-D., 1993. Strong convergence of multivariate point processes of exceedances. Ann. Inst. Statist. Math. 45, 433-444.
18. LeCam, L., Yang, L., 1990. Asymptotics in Statistics. Some Basic Concepts. Springer, New York.
19. Marohn, F., 1995. Contributions to a Local Approach in Extreme Value Statistics. Habilitationsschrift, Katholische Universität Eichstätt.
20. Marohn, F., 1997. Local asymptotic normality in extreme value index estimation. Ann. Inst. Statist. Math. 49, 645-666.
21. Pfanzagl, J., 1994. Parametric Statistical Theory, DeGruyter, Berlin, New York.
22. Press, S.J., 1975. Stable distributions: Probability, inference, and applications in finance - A survey and a review of recent results. In: Patel et al. G.P. (Eds.), Statistical Distributions in Scientific Work. Reidel, Dordrecht, pp. 87-102.
23. Reiss, R.-D., 1993. A Course on Point Processes. Springer, New York.
24. Resnick, S.I., 1987. Extreme Values, Regular Variation, and Point Processes. Springer, New York.
25. Samuelson, P.A., 1976. Limited liability, shortselling, bounded utility, and infinite-variance stable distributions. J. Financial Quart. Anal. 11, 485-503.
26. Strasser, H., 1985. Mathematical Theory of Statistics. DeGruyter, Berlin.