Nonparametric methods for heavy tailed vector data: A survey with applications from finance and hydrology

Recent Advances and Trends in Nonparametric Statistics

Volumn , Issue , 2003, Pages 265-279

  Meerschaert, Mark M ^a   Scheffler, Hans Peter ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84902228782     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044451378-6/50018-1     Document Type: Chapter

References (40)

1. Aban I., Meerschaert M. Shifted Hill's estimator for heavy tails. Comm. Statist. Simulation Comput. 2001, 30:949-962.
2. Aban I., Meerschaert M. Generalized least squares estimators for the thickness of heavy tails. J. Statis. Plann. Inf. 2002, to appear.
3. Adler R., Feldman R., Taqqu M. A Practical Guide to Heavy Tails 1998, Birkhäuser, Amsterdam.
4. Anderson P., Meerschaert M. Modeling river flows with heavy tails. Water Resour. Res. 1998, 34:2271-2280.
5. Benson D., Wheatcraft S., Meerschaert M. Application of a fractional advection-dispersion equation. Water Resour. Res. 2000, 36:1403-1412.
6. Benson D., Schumer R., Meerschaert M., Wheatcraft S. Fractional dispersion, Lévy motions, and the MADE tracer tests. Transport Porous Med. 2001, 42:211-240.
7. Blumen A., Zumofen G., Klafter J. Transport aspects in anomalous diffusion: Lévy walks. Phys Rev. A 1989, 40:3964-3973.
8. Drees H.L.de Haan, Resnick S. How to make a Hill plot. Ann. Statist. 2000, 28:254-274.
9. Fama E. The behavior of stock market prices. J. Business 1965, 38:34-105.
10. Feller W. An Introduction to Probability Theory and Its Applications 1971, Wiley, Boston. 2nd Ed.
11. Gnedenko B., Kolmogorov A. Limit Distributions for Sums of Independent Random Variables 1968, Addison-Wesley, New York.
12. Hall P. On some simple estimates of an exponent of regular variation. J. Royal Statist. Soc. B 1982, 44:37-42.
13. Hill B. A simple general approach to inference about the tail of a distribution. Ann. Statist. 1975, 3:1163-1173.
14. Hosking J., Wallis J. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 1987, 29:339-349.
15. Jansen D., de Vries C. On the frequency of large stock market returns: Putting booms and busts into perspective. Rev. Econ. Statist. 1991, 23:18-24.
16. Jurek Z.J. Polar Coordinates in Banach Spaces. Bull. Ac. Pol. Math. 1984, 32:61-66.
17. Jurek Z., Mason J.D. Operator-Limit Distributions in Probability Theory 1993, Wiley, Reading, Mass.
18. Klafter J., Blumen A., Shlesinger M. Stochastic pathways to anomalous diffusion. Phys. Rev. A 1987, 35:3081-3085.
19. Kozubowski T.J., Meerschaert M.M., Panorska A.K., Scheffler H.P. Operator geometric stable laws 2003, preprint.
20. Kozubowski T.J., Meerschaert M.M., Scheffler H.P. The operator v-stable laws 2003, preprint.
21. Loretan M., Phillips P. Testing the covariance stationarity of heavy tailed time series. J. Empirical Finance 1994, 1:211-248.
22. Mandelbrot B. The variation of certain speculative prices. J. Business 1963, 36:394-419.
23. McCulloch J. Measuring tail thickness to estimate the stable index α: A critique. J. Business Econ. Statist. 1997, 15:74-81.
24. Meerschaert M. Moments of random vectors which belong to some domain of normal attraction. Ann. Probab. 1990, 18:870-876.
25. Meerschaert M., Scheffler H.P. A simple robust estimator for the thickness of heavy tails. J. Statist. Plann. Inf. 1998, 71:19-34.
26. Meerschaert M., Scheffler H.P. Moment estimator for random vectors with heavy tails. J. Multivariate Anal. 1999, 71:145-159.
27. Meerschaert M., Scheffler H.P. Limit Theorems for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice 2001, Wiley, New York.
28. Meerschaert M., Scheffler H.P. Sample cross-correlations for moving averages with regularly varying tails. J. Time Series Anal. 2001, 22(no. 4):481-492.
29. Meerschaert M.M., Scheffler H.P. Portfolio modeling with heavy tailed random vectors. Handbook of Heavy Tailed Distributions in Finance 2003, Elsevier Science, New York. S.T. Rachev (Ed.).
30. Nikias C., Shao M. Signal Processing with Alpha Stable Distributions and Applications 1995, Wiley.
31. Nolan J., Panorska A., McCulloch J.H. Estimation of stable spectral measures. Math. Comput. Modelling 2001, 34(no. 9-11):1113-1122.
32. Painter S., Cvetkovic V., Selroos J. Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport. Geophysical Research Letters 2002, 29(no. 14).
33. Rachev S., Mittnik S. Stable Paretian Models in Finance 2000, Wiley, New York.
34. Resnick S., Stǎricǎ C. Consistency of Hill's estimator for dependent data. J. Appl. Probab. 1995, 32:139-167.
35. Samorodnitsky G., Taqqu M. Stable non-Gaussian Random Processes 1994, Chapman & Hall, Chichester.
36. Scheffler H.P. On estimation of the spectral measure of certain nonnormal operator stable laws. Statist. Probab. Lett. 1999, 43:385-392.
37. Sharpe M. Operator-stable probability distributions on vector groups. Trans. Amer. Math. Soc. 1969, 136:51-65.
38. Shlesinger M., Zaslavsky G., Frisch U. Lévy flights and related topics in physics. Lecture Notes in Physics 1994, 450. Springer-Verlag, New York.
39. Tessier Y., Lovejoy S., Hubert P., Schertzer D. Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions. J. Geophys. Res. 1996, 101:427-440.
40. Uchaikin V., Zolotarev V. Chance and Stability: Stable Distributions and Their Applications 1999, VSP, Berlin.