Efficient estimation of the shape parameter in pareto models with partially known scale

Statistics and Risk Modeling

Volumn 15, Issue 3, 1997, Pages 229-240

  Falk, Michael ^a   Marohn, Frank ^a  

^a CATHOLIC UNIVERSITY OF EICHSTÄTT INGOLSTADT   (Germany)

Author keywords

x03B4; neighborhood; asymptotic efficiency; central sequence; extreme order statistic; finite sample size properties; Generalized Pareto distribution; Hill estimator; LAN; stable distribution

Indexed keywords

EID: 0009221169     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.1997.15.3.229     Document Type: Article

References (20)

1. Chambers, J. M., Mallows, C. L. and Stuck, B. W.: A method for simulating stable random variables. Journal of the American Statistical Association 71 (1976), 340-344
2. DeHaan, L. and Resnick, S. I.: A simple asymptotic estimate for the index of a stable distribution. J. R. Statist. Soc. B 42 (1980), 83-87
3. DuMouchel, W. H.: On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution. Ann. Statist. 1 (1973), 948-957
4. DuMouchel, W. H.: Estimating the stable indexα in order to measure tail thickness: a critique. Ann. Statist. 11 (1983), 1019-1031
5. Falk, M.: LAN of extreme order statistics. Ann. Inst. Statist. Math. 47 (1995), 693-717
6. Falk, M.: On testing the extreme value index via the POT-method. Ann. Statist. 23 (1995), 2013-2035
7. Falk, M. and Marohn, F.: Von Mises conditions revisited. Ann. Probab. 21 (1993), 1310-1328
8. Falk, M., Hüsler, J. and Reiss, R. -D.: Laws of Small Numbers: Extremes and Rare Events. Birkhauser DMV Seminar, Birkhauser, Basel, 1994
9. Feller, W. F.: An Introduction to Probability Theory and its Applications, Vol. II (2nd ed.). Wiley, New York, 1971
10. Galambos, J.: The Asymptotic Theory of Extreme Order Statistics. 2nd edition, Krieger, Malabar, 1987
11. Hall, P.: On some simple estimates of an exponent of regular variation. J. R. Statist. Soc. B 44 (1982), 37-42
12. Hill, B. M.: A simple general approach to inference about the tail of a distribution. Ann. Statist. 13 (1975), 331-341
13. Höpfner, R.: On tail parameter estimation in certain point process models. J. Statist. Planning and Inference (1994), to appear.
14. Höpfner, R.: Estimating a stability parameter: asymptotics and simulations. Preprint Universität Freiburg (1995)
15. Höpfner, R. and Jacod, J.: Some remarks on the joint estimation of the index and the scale parameter for stable processes. In: Asymptotic Statistics (P. Mandl and M. Huskova eds.). Proceedings of the Fifth Prague Symposium 1993. Physica, Heidelberg, 1994, 273-284
16. Höpfner, R. and Rüschendorf, L.: Comparison of estimators in stable models. Preprint Universität Freiburg (1996)
17. Kaufmann, E.: Von Mises conditions,δ-neighborhoods and rates of convergence for maxima. Statist. Probab. Letters 25 (1995), 63-70
18. LeCam, L. and Yang, L.: Asymptotics in Statistics. Some Basic Concepts. Springer Series in Statistics, New York, 1990
19. Marohn, F.: Contributions to a Local Approach in Extreme Value Statistics. Habilita-tionsschrift, Katholische Universität Eichstätt (1995)
20. Teugels, J. L.: Extreme values in insurance mathematics. In Statistical Extremes and Applications. (J. Tiago de Oliveira ed.) NATO ASI Series. Reidel, Dordrecht, 1984, 253-259