On robust tail index estimation

Computational Statistics and Data Analysis

Volumn 56, Issue 11, 2012, Pages 3430-3443

  Beran, Jan ^a   Schell, Dieter ^a  

^a UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

Hill estimator; Huberization; Influence functional; Robust estimation; Small sample; Tail index estimation

Indexed keywords

HILL ESTIMATOR; HUBERIZATION; INFLUENCE FUNCTIONAL; ROBUST ESTIMATION; SMALL SAMPLES; TAIL INDEX;

APPROXIMATION THEORY; FISHER INFORMATION MATRIX;

ESTIMATION;

EID: 84862025758     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.05.028     Document Type: Article

References (33)

1. J. Beirlant, G. Dierckx, Y. Goegebeur, and G. Matthys Tail index estimation and exponential regression model Extremes 2 1999 177 200
2. J. Beran On Heavy Tail Modeling and Teletraffic Data by S.I. Resnick The Annals of Statistics 25 5 1997 1852 1855
3. I. Berkes, L. Horváth, and P. Kokoszka Estimation of the maximal moment exponent of a GARCH(1,1) sequence Econometric Theory 19 4 2003 565 586
4. V. Brazauskas, and R. Serfling Small sample performance of robust estimators of tail parameters for pareto and exponential models Journal of Statistical Computation and Simulation 70 2001 1 19
5. V. Brazauskas, and R. Serfling Robust and efficient estimation of the tail index of a single-parameter Pareto distribution North American Actuarial Journal 4 4 2000 12 27
6. F. Caeiro, M.I. Gomes, and D. Pestana Direct reduction of bias of the classical hill estimator Revstat 3 2 2005 113 136
7. P. Embrechts, H. Furrer, and R. Kaufmann Quantifying regulatory capital for operational risk Derivatives Use, Trading & Regulation 9 3 2003 217 233
8. P. Embrechts, C. Klüppelberg, and T. Mikosch Modelling Extremal Events 1997 Springer New York
9. A. Feuerverger, and P. Hall Estimating a tail exponent by modelling departure from a pareto distribution The Annals of Statistics 27 1999 760 781
10. M. Finkelstein, H.G. Tucker, and J.A. Veeh Pareto tail index estimation revisited North American Actuarial Journal 10 1 2006 1 10
11. M.I. Fraga Alves, M.I. Gomes, and L.de Haan A new class of semi-parametric estimators of the second order parameter Portugaliae Mathematica 60 1 2003 193 213
12. Geluk, J.; de Haan, L.; 1987. Regular Variation, Extensions and Tauberian Theorems. CWI Tract 40. Centre for Mathematics and Computer Science, Amsterdam, The Netherlands.
13. M.I. Gomes, M.J. Martins, and M. Neves Improving second order reduced bias extreme value index estimation Revstat 5 2 2007 177 207
14. M.I. Gomes, and M.J. Martins Bias reduction and explicit estimation of the extreme value index Journal of Statistical Planning and Inference 123 2004 361 378
15. M.I. Gomes, M.J. Martins, and M. Neves Alternatives to a semi-parametric estimators of parameters of rare events: the Jackknife methodology Extremes 3 2000 207 229
16. J. Gustafsson, J.P. Nielsen, P. Pritchard, and D. Roberts Quantifying operational risk guided by kernel smoothing and continuous credibility: a practitioner's view Journal of Operational Risk 1 1 2006 43 55
17. L.de Haan, and L. Peng Comparison of tail index estimators Statistica Neerlandica 52 1998 60 70
18. P. Hall On some simple estimates of an exponent of regular variation Journal of the Royal Statistical Society. Series B 44 1 1982 37 42
19. P. Hall, and A.H. Welsh Adaptive estimates of parameters of regular variation The Annals of Statistics 13 1985 331 341
20. F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel Robust Statistics: The Approach Based on Influence Functions 1986 Wiley New York
21. B. Hill A simple general approach to inference about the tail of a distribution The Annals of Statistics 3 1975 1163 1174
22. P.H. Hsieh Robustness of tail index estimation Journal of Computational and Graphical Statistics 8 2 1999 318 332
23. P.J. Huber Robust Statistics 1981 Wiley New York
24. R. Huisman, K.G. Koedijk, C.J.M. Kool, and F. Palm Tail-index estimates in small samples Journal of Business & Economic Statistics 19 2 2001 208 216
25. Iglesias, E.M.; Linton, O.B.; 2009. Estimation of tail thickness parameters from GJR-GARCH models. Working Paper 09-47. Economic Series (26), Universidad Carlos III, Madrid.
26. D. Mason Laws of large numbers of sums of extreme values The Annals of Probability 10 1982 168 177
27. S. Müller, and K. Rufibach Smooth tail index estimation Journal of Statistical Computation and Simulation 79 9 2009 1155 1167
28. L. Peng Asymptotically unbiased estimator of the extreme-value index Statistic and Probability Letters 38 1998 107 115
29. S. Resnick Heavy tail modelling and teletraffic data: special invited papr The Annals of Statistics 25 5 1997 1805 1869
30. R.J. Serfling Approximation Theorems of Mathematical Statistics 1980 John Wiley & Sons New York
31. B. Vandewalle, J. Beirlant, A. Christmann, and M. Hubert A robust estimator for the tail index of Pareto-type distributions Computational Statistics & Data Analysis 51 12 2007 6252 6268
32. N. Wagner, and T.A. Marsh Tail index estimation in small samples. Simulation results for independent and ARCH-type financial return models Statistical Papers 45 4 2004 545 561
33. N. Wagner, and T.A. Marsh Measuring tail thickness under GARCH and an application to extreme exchange rate changes Journal of Empirical Finance 12 2005 165 185