The qq-estimator and heavy tails

Communications in Statistics. Part C: Stochastic Models

Volumn 12, Issue 4, 1996, Pages 699-724

  Kratz, Marie ^a   Resnick, Sidney I ^a,b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b School of Operations Research and Industrial Engineering   (United States)

Author keywords

Consistency; Heavy tails; Parameter estimation; Qq plot; Regular variation; Time series analysis; Weak convergence

Indexed keywords

EID: 0000562848     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326349608807407     Document Type: Article

References (23)

1. Bingham,N., Goldie, C. and Teugels, J., Regular Variation, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1987.
2. Castillo, E., Extreme Value Theory in Engineering, Academic Press, San Diego, California, 1988.
3. Csörgö, M., Csörgo, S., Horváth, L. and Mason, D., Weighted Empirical and quantile processes, Ann. Probability 14 (1986), 31-85.
4. Csörgö, S., Deheuvels, P. and Mason D., Kernel Estimates of the tail index of a distribution, Ann. Statist. 13 (1985), 1050-1077.
5. Dekkers, A. and Haan, L. de, On the estimation of the extreme value index and large quantile estimation, Ann. Statist. 17 (1989), 1795-1832.
6. Duffy, D., McIntosh, A., Rosenstein, M., and Willinger, W., Analyzing telecommunications traffic data from working common channel signaling subnetworks, Proceedings of the 25th Interface, San Diego Ca (1993).
7. Duffy, D., McIntosh, A., Rosenstein, M., and Willinger, W., Statistical analysis of CCSN/SS7 traffic data from working CCS subnetworks, IEEE Journalen Selected Areas in Communications 12 (1994), 544-551.
8. Feigin, P. Resnick, S. and Stǎricǎ, Cǎtǎlin, Testing for independence in heavy tailed and positive innovation time series, Stochastic Models 11 (1995), 587-612.
9. Haan, L. de, Extreme Value Statistics, Lecture Notes, Econometric Institute, Erasmus University, Rotterdam (1991).
10. Geluk, J. and Haan, L. de, Regular Variation, Extensions and Tauberian Theorems, CWI Tract 40, Center for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands, 1987.
11. Haan, L. de and Stadtmüller, U., Generalized regular variation of second order, Forthcoming: J. Austr. Math. Soc., Preprint, Econometric Institute, Erasmus University Rotterdam (1995).
12. Hill, B., A simple approach to inference about the tail of a distribution, Ann. Statist. 3 (1975), 1163-1174.
13. Jansen, D. and de Vries, C., On the frequency of large stock returns: putting booms and busts into perspective, The Review of Economics and Statistics LXXIII, No 1 (1991), 18-24.
14. Koedijk, K., Schafgans, M. and de Vries, C., The tail index of exchange rate returns, Journal of International Economics 29 (1990), 93-108.
15. Mason, D., Laws of large numbers for sums of extreme values, Ann. Probability 10 (1982), 754-764.
16. Meier-Hellstern, K., Wirth, P., Yan, Y., Hoeflin, D., Traffic models for ISDN data users: office automation application, Teletraffic and Datatraffic in a Period of Change. Proceedings of the 13th ITC (A. Jensen and V.B. Iversen, eds.), North Holland, Amsterdam, The Netherlands, 1991, pp. 167-192.
17. Port, Sidney, Theoretical Probability for Applications, John Wiley & Sons, New York, 1994.
18. Resnick, S., Adventures in Stochastic Processes, Birkhauser, Boston, 1992.
19. Resnick, Sidney and Stǎricǎ, Cǎtǎlin, Consistency of Hill's estimator for dependent data, Preprint: School of ORIE, Cornell University, ETC Building, Ithaca, NY 14853, USA, J. Applied Probability (1995a).
20. Resnick, S. and Stǎricǎ, Cǎtǎlin, Smoothing the Hill estimator, To appear: J. Applied Probability (1995b).
21. Rice, J., Mathematical Statistics and Data Analysis, Brooks/Cole Publishing, Pacific Grove, Calififornia, 1988.
22. Smirnov, N.V., Limit distributions for the terms of a variational series, Amer. Math. Soc. Transl. Ser. I 11 (1952), 82-143.
23. Vervaat, W., Functional central limit theorems for processes with positive drift and their inverses, Z. Wahrscheinlichkeitstheory verw. Geb. 23 (1972), 249-253.