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Abelian and Tauberian theorems on the bias of the Hill Estimator (2001)  (Make Corrections)  
Johan Segers



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Abstract: The bias of Hill's estimator for the positive extreme value index of a distribution is investigated in relation with the convergence rate in the regular variation property of the tail function of the common distribution of the sample and the corresponding tail quantile function. Based on the theory of generalised regular variation, natural second-order conditions are proposed which both imply and are implied by convergence of the expectation of Hill's estimator to the extreme value index at... (Update)

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BibTeX entry:   (Update)

@misc{ segers-abelian,
  author = "Johan Segers",
  title = "Abelian and Tauberian theorems on the bias of the Hill Estimator",
  url = "citeseer.ist.psu.edu/article/segers01abelian.html" }
Citations (may not include all citations):
164   Regular Variation (context) - Bingham, Goldie et al. - 1987
67   A simple general approach to inference about the tail of a d.. (context) - Hill - 1975
55   Modelling Extremal Events (context) - Embrechts, Kluppelberg et al. - 1997
30   On some simple estimates of an exponent of regular variation (context) - Hall - 1982
20   Smoothing the Hill estimator (context) - Resnick, Starica - 1997
18   Practical Analysis of Extreme Values (context) - Beirlant, Teugels et al. - 1996
16   Estimating tails of probability distributions (context) - Smith - 1987
16   Limiting forms of the frequency distribution in the largest .. (context) - Fisher, Tippett - 1928
14   A moment estimator for the index of an extreme-value distrib.. (context) - Dekkers, Einmahl et al. - 1989
12   Optimal choice of sample fraction in extreme-value estimatio.. (context) - Dekkers, de Haan - 1993
12   Geometrizing rates of convergence (context) - Donoho, Liu - 1991
12   Tail estimates motivated by extreme value theory (context) - Davis, Resnick - 1984
11   the estimation of the extremevalue index and large quantile .. (context) - Dekkers, de Haan - 1989
11   Regular variation (context) - Geluk, de Haan - 1987
11   Sur la distribution limite du terme maximum d'une s'erie al'.. (context) - Gnedenko - 1943

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Residual Estimators - Segers (2000)   (Correct)
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