Semi-parametric tail inference through probability-weighted moments

Journal of Statistical Planning and Inference

Volumn 141, Issue 2, 2011, Pages 937-950

  Caeiro, Frederico ^a   Ivette Gomes, M ^b  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

^b Center of Statistics Applications of Lisbon University CEAUL   (Portugal)

Author keywords

Extreme value index; First order scale parameter; Heavy tails; Semi parametric estimation; Statistics of extremes

Indexed keywords

EID: 78649358293     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2010.08.015     Document Type: Article

References (37)

1. Araújo Santos P., Fraga Alves M.I., Gomes M.I. Peaks over random threshold methodology for tail index and quantile estimation. Revstat 2006, 4(3):227-247.
2. Balkema A.A., de Haan L. Residual life time at great age. Ann. Probab. 1974, 2:792-804.
3. Bingham N.H., Goldie C.M., Teugels J.L. Regular Variation 1987, Cambridge University Press.
4. Caeiro F., Gomes M.I. Semi-parametric second-order reduced-bias high quantile estimation. Test 2009, 18(2):392-413.
5. Caeiro F., Gomes M.I., Pestana D. Direct reduction of bias of the classical Hill estimator. Revstat 2005, 3(2):113-136.
6. Csörgo S., Viharos L. Asymptotic normality of least squares estimators of tail indices. Bernoulli 1997, 3:351-370.
7. Csörgo S., Viharos L. Estimating the tail index. Asymptotic Methods in Probability and Statistics 1998, 833-881. North-Holland, Amsterdam. Szyskowicz (Ed.).
8. Csörgo S., Deheuvels P., Mason D. Kernel estimates of the tail index of a distribution. Ann. Statist. 1985, 13:1050-1077.
9. David H., Nagaraja H.N. Order Statistics 2003, John Wiley & Sons.
10. Dekkers A., de Haan L. Optimal sample fraction in extreme value estimation. J. Multivariate Anal. 1993, 47(2):173-195.
11. Diebolt J., Guillou A., Rached I. A new look at probability-weighted moments estimators. C.R. Math. 2004, 338:629-634.
12. Diebolt J., Guillou A., Rached I. Approximation of the distribution of excesses through a generalized probability-weighted moments method. J. Statist. Plann. Inference 2007, 137:841-857.
13. Diebolt J., Guillou A., Ribereau P. Asymptotic normality of extreme quantile estimators based on the peaks-over-threshold approach. Comm. Statist.-Theory and Methods 2007, 36:869-886.
14. Diebolt J., Guillou A., Naveau P., Ribereau P. Improving probability-weighted moment methods for the generalized extreme value distribution. Revstat 2008, 6(1):33-50.
15. Gnedenko B.V. Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 1943, 44:423-453.
16. Gomes M.I., Martins M.J. Generalizations of the Hill estimator-asymptotic versus finite sample behaviour. J. Statist. Plann. Inference 2001, 93:161-180.
17. Gomes M.I., Neves C. Asymptotic comparison of the mixed moment and classical extreme value index estimators. Statist. Probab. Lett. 2008, 78(6):643-653.
18. Gomes M.I., Pestana D. A sturdy reduced bias extreme quantile (VaR) estimator. J. Amer. Statist. Assoc. 2007, 102(477):280-292.
19. Gomes M.I., Figueiredo F., Mendonça S. Asymptotically best linear unbiased tail estimators under a second-order regular variation condition. J. Statist. Plann. Inference 2005, 134:409-433.
20. Gomes M.I., Miranda C., Pereira H. Revisiting the role of the Jackknife methodology in the estimation of a positive extreme value index. Comm. Statist.-Theory and Methods 2005, 34:1-20.
21. Gomes M.I., Martins M.J., Neves M.M. Improving second order reduced bias extreme value index estimation. Revstat 2007, 5(2):177-207.
22. Gomes M.I., Miranda C., Viseu C. Reduced bias extreme value index estimation and the Jackknife methodology. Statist. Neerlandica 2007, 61(2):243-270.
23. Gomes M.I., Canto e Castro L., Fraga Alves M.I., Pestana D. Statistics of extremes for iid data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions. Extremes 2008, 11(1):3-34.
24. Gomes M.I., Fraga Alves M.I., Araújo Santos P. PORT Hill and moment estimators for heavy-tailed models. Comm. Statist.-Simulation Comput. 2008, 37:1281-1306.
25. Gomes M.I., de Haan L., Henriques-Rodrigues L. Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses. J. R. Statist. Soc. 2008, B70(1):31-52.
26. Greenwood J.A., Landwehr J.M., Matalas N.C., Wallis J.R. Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water Resour. Res. 1979, 15:1049-1054.
27. de Haan L., Ferreira A. Extreme Value Theory: an Introduction 2006, Springer Science+Business Media, LLC, New York.
28. de Haan L., Peng L. Comparison of tail index estimators. Statist. Neerlandica 1998, 52:60-70.
29. Hill B.M. A simple general approach to inference about the tail of a distribution. Ann. Statist. 1975, 3(5):1163-1174.
30. Hosking J., Wallis J. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 1987, 29(3):339-349.
31. Hosking J., Wallis J., Wood E. Estimation of the generalized extreme value distribution by the method of probability-weighted moments. Technometrics 1985, 27(3):251-261.
32. Kratz M., Resnick S. The QQ-estimator of the index of regular variation. Comm. Statist.-Stoch. Models 1996, 12:699-724.
33. Landwher J., Matalas N., Wallis J. Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resour. Res. 1979, 15:1055-1064.
34. Oliveira O., Gomes M.I., Fraga Alves M.I. Improvements in the estimation of a heavy tail. Revstat 2006, 4(2):81-109.
35. Pickands J. Statistical inference using extreme order statistics. Ann. Statist. 1975, 3:119-131.
36. Schulze J., Steinbach J. On least squares estimates of an exponential tail coefficient. Statist. Decisions 1996, 14:353-372.
37. Weissman I. Estimation of parameters of large quantiles based on the k largest observations. J. Amer. Statist. Assoc. 1978, 73:812-815.