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Volumn 76, Issue , 2008, Pages 23-31

A location invariant moment-type estimator. I

Author keywords

Extreme value index; Location invariant property; Moment estimation; Order statistics; Regular varying functions; Strong and weak consistencies

Indexed keywords


EID: 85009808183     PISSN: 00949000     EISSN: 15477363     Source Type: Journal    
DOI: 10.1090/S0094-9000-08-00728-X     Document Type: Article
Times cited : (4)

References (29)
  • 1
    • 0035535918 scopus 로고    scopus 로고
    • Penultimate approximation for Hill’s estimator
    • MR1858418 (2002h:62156)
    • S. Cheng and L. de Haan, Penultimate approximation for Hill’s estimator, Scand. J. Statist. 28 (2001), 569–575.MR1858418 (2002h:62156)
    • (2001) Scand. J. Statist , vol.28 , pp. 569-575
    • Cheng, S.1    De Haan, L.2
  • 2
    • 0032339702 scopus 로고    scopus 로고
    • Asymptotic expansions of estimators for the tail index with applications
    • MR1666796 (2000d:62079)
    • S. Cheng and J. Pan, Asymptotic expansions of estimators for the tail index with applications, Scand. J. Statist. 25 (1998), 717–728.MR1666796 (2000d:62079)
    • (1998) Scand. J. Statist , vol.25 , pp. 717-728
    • Cheng, S.1    Pan, J.2
  • 4
    • 0003032284 scopus 로고
    • Slow variation and characterization of domains of attraction
    • Vimeiro, Reidel, Dordrecht, 1984, MR784812 (87b:60036)
    • L. de Haan, Slow variation and characterization of domains of attraction, Statistical Extremes and Applications, Vimeiro, 1983, Reidel, Dordrecht, 1984, pp. 31–48.MR784812 (87b:60036)
    • (1983) Statistical Extremes and Applications , pp. 31-48
    • De Haan, L.1
  • 5
    • 0039470514 scopus 로고    scopus 로고
    • Generalized regular variation of second order
    • MR1420345 (97g:26001)
    • L. de Haan and U. Stadtmüller, Generalized regular variation of second order, J. Aust. Math. Soc., A 61 (1996), 381–395.MR1420345 (97g:26001)
    • (1996) J. Aust. Math. Soc., A , vol.61 , pp. 381-395
    • De Haan, L.1    Stadtmüller, U.2
  • 6
    • 0001760675 scopus 로고
    • A moment estimator for the index of an extreme-value distribution
    • MR1026315 (91i:62033)
    • A. L. M. Dekkers, J. H. J. Einmahl, and L. de Haan, A moment estimator for the index of an extreme-value distribution, Ann. Stat. 17 (1989), 1833–1855.MR1026315 (91i:62033)
    • (1989) Ann. Stat , vol.17 , pp. 1833-1855
    • Dekkers, A.L.M.1    Einmahl, J.H.J.2    De Haan, L.3
  • 7
    • 0040828799 scopus 로고
    • Refined Pickands estimators of the extreme value index
    • MR1389865 (97d:62069)
    • H. Drees Refined Pickands estimators of the extreme value index, Ann. Statist. 23 (1995), 2059–2080.MR1389865 (97d:62069)
    • (1995) Ann. Statist , vol.23 , pp. 2059-2080
    • Drees, H.1
  • 8
    • 0032484340 scopus 로고    scopus 로고
    • A general class of estimators of the extreme value index
    • MR1616999 (99c:62085)
    • H. Drees, A general class of estimators of the extreme value index, J. Statist. Plann. Inference 66 (1998), 95–112.MR1616999 (99c:62085)
    • (1998) J. Statist. Plann. Inference , vol.66 , pp. 95-112
    • Drees, H.1
  • 9
    • 0001061726 scopus 로고    scopus 로고
    • Selecting the optimal sample fraction in univariate extreme value index
    • MR1632189 (99h:62034)
    • H. Drees and E. Kaufmann, Selecting the optimal sample fraction in univariate extreme value index, Stochastic Process. Appl. 75 (1998), 149–172.MR1632189 (99h:62034)
    • (1998) Stochastic Process. Appl , vol.75 , pp. 149-172
    • Drees, H.1    Kaufmann, E.2
  • 10
    • 1642341600 scopus 로고    scopus 로고
    • Estimation problems for distributions with heavy tails
    • MR2058119 (2005c:62059)
    • Z. Fan, Estimation problems for distributions with heavy tails, J. Statist. Plann. Inference 123 (2004), 13–40.MR2058119 (2005c:62059)
    • (2004) J. Statist. Plann. Inference , vol.123 , pp. 13-40
    • Fan, Z.1
  • 11
    • 8344233641 scopus 로고    scopus 로고
    • A location invariant Hill-type estimator
    • MR1907061 (2003d:62129)
    • M. I. Fraga Alves, A location invariant Hill-type estimator, Extremes 4 (2001), 199–217.MR1907061 (2003d:62129)
    • (2001) Extremes , vol.4 , pp. 199-217
    • Fraga Alves, M.I.1
  • 12
    • 0003326493 scopus 로고
    • Regular variation, extensions, and Tauberian theorems
    • MR906871 (89a:26002)
    • J. L. Geluk and L. de Haan, Regular variation, extensions, and Tauberian theorems, CWI Tract 40 (1987).MR906871 (89a:26002)
    • (1987) CWI Tract , vol.40
    • Geluk, J.L.1    De Haan, L.2
  • 13
    • 0000866457 scopus 로고    scopus 로고
    • Generalizations of the Hill estimator-asymptotic versus finite sample behavior
    • MR1822394
    • M. I. Gomes and M. J. Martins, Generalizations of the Hill estimator-asymptotic versus finite sample behavior, J. Statist. Plann. Inference 93 (2001), 161–180.MR1822394
    • (2001) J. Statist. Plann. Inference , vol.93 , pp. 161-180
    • Gomes, M.I.1    Martins, M.J.2
  • 14
    • 0347759854 scopus 로고    scopus 로고
    • Censoring estimators of a positive tail index
    • MR2018025 (2005d:62155)
    • M. I. Gomes and O. Oliveira, Censoring estimators of a positive tail index, Statist. Probab. Lett. 65 (2003), 147–159.MR2018025 (2005d:62155)
    • (2003) Statist. Probab. Lett , vol.65 , pp. 147-159
    • Gomes, M.I.1    Oliveira, O.2
  • 15
    • 0000439164 scopus 로고
    • On estimating the endpoint of a distribution
    • MR653530 (83f:62043)
    • P. Hall, On estimating the endpoint of a distribution, Ann. Statist. 10 (1982), 556–568.MR653530 (83f:62043)
    • (1982) Ann. Statist , vol.10 , pp. 556-568
    • Hall, P.1
  • 16
    • 0001263124 scopus 로고
    • A simple general approach to inference about the tail of a distribution
    • MR0378204 (51:14373)
    • B. M. Hill, A simple general approach to inference about the tail of a distribution, Ann. Statist. 3 (1975), 1163–1174.MR0378204 (51:14373)
    • (1975) Ann. Statist , vol.3 , pp. 1163-1174
    • Hill, B.M.1
  • 17
    • 22044439647 scopus 로고    scopus 로고
    • Some results on estimation of the tail index of a distribution
    • MR1655939 (2000a:62037)
    • J. Pan, Some results on estimation of the tail index of a distribution, Chinese Ann. Math. Ser. B 19 (1998), 239–248.MR1655939 (2000a:62037)
    • (1998) Chinese Ann. Math. Ser. B , vol.19 , pp. 239-248
    • Pan, J.1
  • 18
    • 85009781322 scopus 로고    scopus 로고
    • Extension of Pickands’ estimator
    • MR1612631 (99c:62111)
    • Z. Peng, Extension of Pickands’ estimator, Math. Sinica 40 (1997), 759–762.MR1612631 (99c:62111)
    • (1997) Math. Sinica , vol.40 , pp. 759-762
    • Peng, Z.1
  • 19
    • 0032087519 scopus 로고    scopus 로고
    • Asymptotically unbiased estimators for the extreme value index
    • MR1627906 (99e:62056)
    • L. Peng, Asymptotically unbiased estimators for the extreme value index, Statist. Probab. Lett. 38 (1998), 107–115.MR1627906 (99e:62056)
    • (1998) Statist. Probab. Lett , vol.38 , pp. 107-115
    • Peng, L.1
  • 20
    • 0001075431 scopus 로고
    • Statistical inference using extreme order statistics
    • MR0423667 (54:11642)
    • J. Pickands, Statistical inference using extreme order statistics, Ann. Statist. 3 (1975), 119–131.MR0423667 (54:11642)
    • (1975) Ann. Statist , vol.3 , pp. 119-131
    • Pickands, J.1
  • 21
    • 85009761923 scopus 로고
    • Convergence of Pickands-type estimators
    • Y. Qi and S. Cheng, Convergence of Pickands-type estimators, Chinese Sci. Bull. 37 (1992), 1409–1413.
    • (1992) Chinese Sci. Bull , vol.37 , pp. 1409-1413
    • Qi, Y.1    Cheng, S.2
  • 22
    • 0035995090 scopus 로고    scopus 로고
    • Abelian and Tauberian theorems for the bias of the Hill estimator
    • MR1925570 (2003k:62159)
    • J. Segers, Abelian and Tauberian theorems for the bias of the Hill estimator, Scand. J. Statist. 29 (2001), 461–483.MR1925570 (2003k:62159)
    • (2001) Scand. J. Statist , vol.29 , pp. 461-483
    • Segers, J.1
  • 23
    • 8644283685 scopus 로고    scopus 로고
    • Generalized Pickands estimators for the extreme value index
    • MR2102765
    • J. Segers, Generalized Pickands estimators for the extreme value index, J. Statist. Plann. Inference 128 (2005), 381–396.MR2102765
    • (2005) J. Statist. Plann. Inference , vol.128 , pp. 381-396
    • Segers, J.1
  • 24
    • 0000704345 scopus 로고
    • Maximum likelihood estimation in a class of nonregular cases
    • MR790201 (86k:62053)
    • R. L. Smith, Maximum likelihood estimation in a class of nonregular cases, Biometrika 72 (1985), 67–90.MR790201 (86k:62053)
    • (1985) Biometrika , vol.72 , pp. 67-90
    • Smith, R.L.1
  • 25
    • 0001258027 scopus 로고
    • Estimation of tails of probability distribution
    • MR902252 (88j:62096)
    • R. L. Smith, Estimation of tails of probability distribution, Ann. Statist. 15 (1987), 1174–1207.MR902252 (88j:62096)
    • (1987) Ann. Statist , vol.15 , pp. 1174-1207
    • Smith, R.L.1
  • 26
    • 0000110113 scopus 로고
    • Maximum likelihood estimation of the lower tail of probability distribution
    • MR816094 (87b:62035)
    • R. L. Smith and I. Weissman, Maximum likelihood estimation of the lower tail of probability distribution, J. Roy. Statist. Soc. Ser. B 47 (1985), 285–298.MR816094 (87b:62035)
    • (1985) J. Roy. Statist. Soc. Ser. B , vol.47 , pp. 285-298
    • Smith, R.L.1    Weissman, I.2
  • 28
    • 27144531190 scopus 로고    scopus 로고
    • General regular variation of nth order and the second order Edgeworth expansion of the extreme value distribution. I
    • MR2176324 (2006i:60063)
    • X. Wang and S. Cheng, General regular variation of nth order and the second order Edgeworth expansion of the extreme value distribution. I, Acta Math. Sin., Engl. Ser. 21 (2005), no. 5, 1121–1130.MR2176324 (2006i:60063)
    • (2005) Acta Math. Sin., Engl. Ser , vol.21 , Issue.5 , pp. 1121-1130
    • Wang, X.1    Cheng, S.2
  • 29
    • 0036532098 scopus 로고    scopus 로고
    • On a general Pickands estimator of extreme value index
    • MR1896495 (2003e:62050)
    • S. Yun, On a general Pickands estimator of extreme value index, J. Statist. Plann. Inference 102 (2002), 389–409.MR1896495 (2003e:62050)
    • (2002) J. Statist. Plann. Inference , vol.102 , pp. 389-409
    • Yun, S.1


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