Adaptive PORT-MVRB estimation: an empirical comparison of two heuristic algorithms

Journal of Statistical Computation and Simulation

Volumn 83, Issue 6, 2013, Pages 1129-1144

  Gomes, M Ivette ^a   Henriques Rodrigues, Lígia ^b   Fraga Alves, M Isabel ^a   Manjunath, B G ^c  

^a UNIVERSITY OF LISBON   (Portugal)

^b INSTITUTO POLITÉCNICO DE TOMAR   (Portugal)

^c INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

adaptive choices; bias reduction; extreme value index; GARCH processes; heuristic methods; location scale invariant estimation; semi parametric estimation; statistics of extremes

Indexed keywords

EID: 84878971195     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2011.652113     Document Type: Article

References (32)

1. Hill, B. 1975. A simple general approach to inference about the tail of a distribution. Ann. Statist., 3: 1163 - 1174. (doi:10.1214/aos/1176343247)
2. Beirlant, J., Dierckx, G., Goegebeur, Y. and Matthys, G. 1999. Tail index estimation and an exponential regression model. Extremes, 2: 177 - 200. (doi:10.1023/A:1009975020370)
3. Feuerverger, A. and Hall, P. 1999. Estimating a tail exponent by modelling departure from a Pareto distribution. Ann. Statist., 27: 760 - 781. (doi:10.1214/aos/1018031215)
4. Gomes, M. I., Martins, M. J. and Neves, M. M. 2000. Alternatives to a semi-parametric estimator of parameters of rare events - the Jackknife methodology. Extremes, 3 (3): 207 - 229. (doi:10.1023/A:1011470010228)
5. Caeiro, F., Gomes, M. I. and Pestana, D. 2005. Direct reduction of bias of the classical Hill estimator. Revstat, 3 (2): 111 - 136.
6. Gomes, M. I., Martins, M. J. and Neves, M. M. 2007. Improving second order reduced bias extreme value index estimation. Revstat, 5 (2): 177 - 207.
7. Gomes, M. I., de Haan, L. and Henriques-Rodrigues, L. 2008. Tail index estimation for heavy-tailed models: Accommodation of bias in weighted log-excesses. J. R. Stat. Soc. B, 70 (1): 31 - 52.
8. Araújo Santos, P., Fraga Alves, M. I. and Gomes, M. I. 2006. Peaks over random threshold methodology for tail index and quantile estimation. Revstat, 4 (3): 227 - 247.
9. Gomes, M. I., Fraga Alves, M. I. and Araújo Santos, P. 2008. PORT Hill and moment estimators for heavy-tailed models. Comm. Statist. Simulation Comput., 37: 1281 - 1306. (doi:10.1080/03610910802050910)
10. Gomes, M. I., Henriques-Rodrigues, L. and Miranda, C. 2011. Reduced-bias location-invariant extreme value index estimation: A simulation study. Comm. Statist. Simulation Comput, 40 (3): 424 - 447. (doi:10.1080/03610918.2010.543297)
11. Figueiredo, F., Gomes, M. I., Henriques-Rodrigues, L. and Miranda, C. 2011. A computational study of a quasi-PORT methodology for VaR based on second-order reduced-bias estimation. J. Stat. Comput. Simul., doi:10.1080/00949655.2010.547196
12. Henriques-Rodrigues, L. and Gomes, M. I. 2009. High quantile estimation and the PORT methodology. Revstat, 7 (3): 245 - 264.
13. Drees, H. 2003. Extreme quantile estimation for dependent data, with applications to finance. Bernoulli, 9 (4): 617 - 657. (doi:10.3150/bj/1066223272)
14. Gomes, M. I. and Martins, M. J. 2002. 'Asymptotically unbiased' estimators of the tail index based on external estimation of the second order parameter. Extremes, 5 (1): 5 - 31. (doi:10.1023/A:1020925908039)
15. Fraga Alves, M. I., Gomes, M. I. and de Haan, L. 2003. A new class of semi-parametric estimators of the second order parameter. Port. Math, 60 (2): 194 - 213.
16. Gomes, M. I. and Pestana, D. 2007. A simple second order reduced-bias' tail index estimator. J. Stat. Comput. Simul, 77 (6): 487 - 504. (doi:10.1080/10629360500282239)
17. Gomes, M. I. and Pestana, D. 2007. A sturdy reduced-bias extreme quantile (VaR) estimator. J. Amer. Statist. Assoc, 102 (477): 280 - 292. (doi:10.1198/016214506000000799)
18. Goegebeur, Y., Beirlant, J. and de Wet, T. 2008. Linking Pareto-tail kernel goodness-of-fit statistics with tail index at optimal threshold and second order estimation. Revstat, 6 (1): 51 - 69.
19. Goegebeur, Y., Beirlant, J. and de Wet, T. 2010. Kernel estimators for the second order parameter in extreme value statistics. J. Statist. Plann. Inference, 140: 2632 - 2652. (doi:10.1016/j.jspi.2010.03.029)
20. Ciuperca, G. and Mercadier, C. 2010. Semi-parametric estimation for heavy tailed distributions. Extremes, 13 (1): 55 - 87. (doi:10.1007/s10687-009-0086-6)
21. Caeiro, F., Gomes, M. I. and Henriques-Rodrigues, L. 2009. Reduced-bias tail index estimators under a third order framework. Comm. Statist. Theory Methods, 38 (7): 1019 - 1040. (doi:10.1080/03610920802361415)
22. Caeiro, F. and Gomes, M. I. 2006. A new class of estimators of a 'scale' second order parameter. Extremes, 9: 193 - 211. (doi:10.1007/s10687-006-0026-7)
23. Gomes, M. I., Henriques-Rodrigues, L., Pereira, H. and Pestana, D. 2010. Tail index and second order parameters' semi-parametric estimation based on the log-excesses. J. Stat. Comput. Simul, 80 (6): 653 - 666. (doi:10.1080/00949650902755178)
24. Hall, P. 1982. On some simple estimates of an exponent of regular variation. J. R. Stat. Soc. B, 44: 37 - 42.
25. Gomes, M. I. and Oliveira, O. 2001. The bootstrap methodology in statistical extremes - Choice of the optimal sample fraction. Extremes, 4 (4): 331 - 358. (doi:10.1023/A:1016592028871)
26. Gomes, M. I., Pestana, D., Henriques-Rodrigues, L. and Viseu, C. 2008. " Tail behaviour: An empirical study ". In Advances in Mathematical and Statistical Modeling, Edited by: Arnold, B. C., Balakrishnan, N., Sarabia, J. M. and Minguez, R. 195 - 207. Boston: Birkhauser. Chapter 14
27. Gomes, M. I., Figueiredo, F. and Mendonça, S. 2005. Asymptotically best linear unbiased tail estimators under a second order regular variation condition. J. Statist. Plann. Inference, 134 (2): 409 - 433. (doi:10.1016/j.jspi.2004.04.013)
28. McNeil, A. and Frey, R. 2000. Estimation of tail-related risk measures for heteroscedastic financial times series: An extreme value approach. J. Empir. Finance, 7: 271 - 300. (doi:10.1016/S0927-5398(00)00012-8)
29. Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. J. Econ., 31: 307 - 327.
30. Engle, R. F. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50 (4): 987 - 1007. (doi:10.2307/1912773)
31. Box, G. E.P., Jenkins, G. M. and Reinsel, G. C. 1994. Time Series Analysis: Forecasting and Control, 3, Englewood Cliffs, NJ: Prentice-Hall.
32. Jones, M. C. and Faddy, M. J. 2003. A skew extension of the t-distribution, with applications. J. R. Stat. Soc. B, 65 (1): 159 - 174. (doi:10.1111/1467-9868.00378)