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Volumn 11, Issue 3, 2008, Pages 303-328

Tail index estimation for heavy tails: Accommodation of bias in the excesses over a high threshold

Author keywords

Generalized Pareto models; Maximum likelihood estimation; Semi parametric estimation; Statistics of extremes

Indexed keywords


EID: 49249111136     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-008-0059-1     Document Type: Article
Times cited : (5)

References (30)
  • 1
    • 40749128454 scopus 로고    scopus 로고
    • Peaks over random threshold methodology for tail index and quantile estimation
    • 3
    • P. Araújo Santos M.I. Fraga Alves M.I. Gomes 2006 Peaks over random threshold methodology for tail index and quantile estimation Rev. Stat. 4 3 227 247
    • (2006) Rev. Stat. , vol.4 , pp. 227-247
    • Araújo Santos, P.1    Fraga Alves, M.I.2    Gomes, M.I.3
  • 3
    • 34147125324 scopus 로고    scopus 로고
    • A new class of estimators of the "scale" second order parameter
    • F. Caeiro M.I. Gomes 2006 A new class of estimators of the "scale" second order parameter Extremes 9 193 211
    • (2006) Extremes , vol.9 , pp. 193-211
    • Caeiro, F.1    Gomes, M.I.2
  • 4
    • 33947287640 scopus 로고    scopus 로고
    • Direct reduction of bias of the classical Hill estimator
    • 2
    • F. Caeiro M.I. Gomes D. Pestana 2005 Direct reduction of bias of the classical Hill estimator Rev. Stat. 3 2 111 136
    • (2005) Rev. Stat. , vol.3 , pp. 111-136
    • Caeiro, F.1    Gomes, M.I.2    Pestana, D.3
  • 5
    • 0000737722 scopus 로고
    • Modeling excesses over high threshold with an application
    • D. Reidel Dordrecht
    • Davison, A.: Modeling excesses over high threshold with an application. In: Tiago de Oliveira, J. (ed.) Statistical Extremes and Applications, pp. 461-482. D. Reidel, Dordrecht (1984)
    • (1984) Statistical Extremes and Applications , pp. 461-482
    • Davison, A.1    De Oliveira, J.T.2
  • 6
    • 0001080355 scopus 로고
    • Optimal sample fraction in extreme value estimation
    • 2
    • A. Dekkers L. de Haan 1993 Optimal sample fraction in extreme value estimation J. Multivar. Anal. 47 2 173 195
    • (1993) J. Multivar. Anal. , vol.47 , pp. 173-195
    • Dekkers, A.1    De Haan, L.2
  • 8
    • 0032330687 scopus 로고    scopus 로고
    • Comparison of tail index estimators
    • L. de Haan L. Peng 1998 Comparison of tail index estimators Stat. Neerl. 52 60 70
    • (1998) Stat. Neerl. , vol.52 , pp. 60-70
    • De Haan, L.1    Peng, L.2
  • 9
    • 22244474071 scopus 로고    scopus 로고
    • On maximum likelihood estimation of the extreme value index
    • H. Drees A. Ferreira L. de Haan 2004 On maximum likelihood estimation of the extreme value index Ann. Appl. Probab. 14 1179 1201
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 1179-1201
    • Drees, H.1    Ferreira, A.2    De Haan, L.3
  • 11
    • 10244233506 scopus 로고    scopus 로고
    • A new class of semi-parametric estimators of the second order parameter
    • 2
    • M.I. Fraga Alves M.I. Gomes L. de Haan 2003 A new class of semi-parametric estimators of the second order parameter Port. Math. 60 2 193 213
    • (2003) Port. Math. , vol.60 , pp. 193-213
    • Fraga Alves, M.I.1    Gomes, M.I.2    De Haan, L.3
  • 13
    • 0000005110 scopus 로고
    • Sur la distribution limite du terme maximum d'une série aléatoire
    • B.V. Gnedenko 1943 Sur la distribution limite du terme maximum d'une série aléatoire Ann. Math. 44 423 453
    • (1943) Ann. Math. , vol.44 , pp. 423-453
    • Gnedenko, B.V.1
  • 14
    • 0000866457 scopus 로고    scopus 로고
    • Alternatives to Hill's estimator-asymptotic versus finite sample behaviour
    • M.I. Gomes M.J. Martins 2001 Alternatives to Hill's estimator-asymptotic versus finite sample behaviour J. Stat. Plan. Inference 93 161 180
    • (2001) J. Stat. Plan. Inference , vol.93 , pp. 161-180
    • Gomes, M.I.1    Martins, M.J.2
  • 15
    • 33845663439 scopus 로고    scopus 로고
    • "asymptotically unbiased" estimators of the tail index based on external estimation of the second order parameter
    • 1
    • M.I. Gomes M.J. Martins 2002 "Asymptotically unbiased" estimators of the tail index based on external estimation of the second order parameter Extremes 5 1 5 31
    • (2002) Extremes , vol.5 , pp. 5-31
    • Gomes, M.I.1    Martins, M.J.2
  • 16
    • 40749088539 scopus 로고    scopus 로고
    • Asymptotic comparison of the mixed moment and classical extreme value index estimators
    • doi: 10.1016/j,spl.2007.07.026
    • Gomes, M.I., Neves, C.: Asymptotic comparison of the mixed moment and classical extreme value index estimators. Stat. Probab. Lett. (2007). doi: 10.1016/j,spl.2007.07.026
    • (2007) Stat. Probab. Lett.
    • Gomes, M.I.1    Neves, C.2
  • 17
    • 0013127441 scopus 로고    scopus 로고
    • The bootstrap methodology in statistical extremes-the choice of the optimal sample fraction
    • 4
    • M.I. Gomes O. Oliveira 2001 The bootstrap methodology in statistical extremes-the choice of the optimal sample fraction Extremes 4 4 331 358
    • (2001) Extremes , vol.4 , pp. 331-358
    • Gomes, M.I.1    Oliveira, O.2
  • 18
    • 34249049511 scopus 로고    scopus 로고
    • A simple second order reduced-bias' tail index estimator
    • 6
    • M.I. Gomes D. Pestana 2007 A simple second order reduced-bias' tail index estimator J. Stat. Comput. Simul. 77 6 487 504
    • (2007) J. Stat. Comput. Simul. , vol.77 , pp. 487-504
    • Gomes, M.I.1    Pestana, D.2
  • 19
    • 33947256203 scopus 로고    scopus 로고
    • A sturdy second order reduced bias' value at risk estimator
    • 477
    • M.I. Gomes D. Pestana 2007 A sturdy second order reduced bias' value at risk estimator J. Am. Stat. Assoc. 102 477 280 292
    • (2007) J. Am. Stat. Assoc. , vol.102 , pp. 280-292
    • Gomes, M.I.1    Pestana, D.2
  • 20
    • 10244241162 scopus 로고    scopus 로고
    • Semi-parametric estimation of the second order parameter-asymptotic and finite sample behaviour
    • 4
    • M.I. Gomes L. de Haan L. Peng 2002 Semi-parametric estimation of the second order parameter-asymptotic and finite sample behaviour Extremes 5 4 387 414
    • (2002) Extremes , vol.5 , pp. 387-414
    • Gomes, M.I.1    De Haan, L.2    Peng, L.3
  • 21
    • 17044389845 scopus 로고    scopus 로고
    • Revisiting the role of the Jackknife methodology in the estimation of a positive extreme value index
    • M.I. Gomes C. Miranda H. Pereira 2005 Revisiting the role of the Jackknife methodology in the estimation of a positive extreme value index Commun. Stat. Theory Methods 34 1 20
    • (2005) Commun. Stat. Theory Methods , vol.34 , pp. 1-20
    • Gomes, M.I.1    Miranda, C.2    Pereira, H.3
  • 22
    • 39449112523 scopus 로고    scopus 로고
    • Improving second order reduced bias extreme value index estimation
    • 2
    • M.I. Gomes M.J. Martins M. Neves 2007 Improving second order reduced bias extreme value index estimation Rev. Stat. 5 2 177 207
    • (2007) Rev. Stat. , vol.5 , pp. 177-207
    • Gomes, M.I.1    Martins, M.J.2    Neves, M.3
  • 23
    • 34247599297 scopus 로고    scopus 로고
    • Reduced bias extreme value index estimation and the Jackknife methodology
    • 2
    • M.I. Gomes C. Miranda C. Viseu 2007 Reduced bias extreme value index estimation and the Jackknife methodology Stat. Neerl. 61 2 243 270
    • (2007) Stat. Neerl. , vol.61 , pp. 243-270
    • Gomes, M.I.1    Miranda, C.2    Viseu, C.3
  • 24
    • 37849040464 scopus 로고    scopus 로고
    • Tail index estimation for heavy-tailed models: Accommodation of bias in weighted log-excesses
    • 1. doi:10.1007/s10687-007-0048-9, 2007
    • M.I. Gomes L. de Haan L. Henriques Rodrigues 2008 Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses J. R. Stat. Soc. B 70 1 31 52 doi:10.1007/s10687-007-0048-9, 2007
    • (2008) J. R. Stat. Soc. B , vol.70 , pp. 31-52
    • Gomes, M.I.1    De Haan, L.2    Henriques Rodrigues, L.3
  • 25
    • 39449117370 scopus 로고    scopus 로고
    • A heuristic adaptive choise of the threshold for bias-corrected hill estimators
    • doi: 10.1080/10629360600954000
    • Gomes, M.I., Henriques Rodrigues, L., Vandewalle, B., Viseu, C.: A heuristic adaptive choise of the threshold for bias-corrected hill estimators. J. Stat. Comput. Simul. (2008b). doi: 10.1080/10629360600954000
    • (2008) J. Stat. Comput. Simul.
    • Gomes, M.I.1    Henriques Rodrigues, L.2    Vandewalle, B.3    Viseu, C.4
  • 26
    • 84952103052 scopus 로고
    • Computing maximum likelihood estimates for the generalized pareto distribution
    • 2
    • S.D. Grimshaw 1993 Computing maximum likelihood estimates for the generalized pareto distribution Technometrics 35 2 185 191
    • (1993) Technometrics , vol.35 , pp. 185-191
    • Grimshaw, S.D.1
  • 27
    • 0000817285 scopus 로고
    • Adaptive estimates of parameters of regular variation
    • P. Hall A.H. Welsh 1985 Adaptive estimates of parameters of regular variation Ann. Stat. 13 331 341
    • (1985) Ann. Stat. , vol.13 , pp. 331-341
    • Hall, P.1    Welsh, A.H.2
  • 28
    • 0001263124 scopus 로고
    • A simple general approach to inference about the tail of a distribution
    • B.M. Hill 1975 A simple general approach to inference about the tail of a distribution Ann. Stat. 3 1163 1174
    • (1975) Ann. Stat. , vol.3 , pp. 1163-1174
    • Hill, B.M.1
  • 29
    • 0000374975 scopus 로고
    • On the theory of order statistics
    • A. Rényi 1953 On the theory of order statistics Acta Math. Sci. Hungar. Tomus IV 191 227
    • (1953) Acta Math. Sci. Hungar. Tomus , vol.4 , pp. 191-227
    • Rényi, A.1
  • 30
    • 0001258027 scopus 로고
    • Estimating tails of probability distributions
    • 3
    • R.L. Smith 1987 Estimating tails of probability distributions Ann. Stat. 15 3 1174 1207
    • (1987) Ann. Stat. , vol.15 , pp. 1174-1207
    • Smith, R.L.1


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