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• W1985514006 abstract "Previous article Next article The Asymptotic Behavior of Hill’s EstimatorJ. Beirlant and J. K. TeugelsJ. Beirlant and J. K. Teugelshttps://doi.org/10.1137/1131060PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. Z. Arov and , A. A. Bobrov, The extreme terms of a sample and their role in a sum of independent variables, Theory Probab. Appl., 4 (1960), 377–396 0098.11202 LinkGoogle Scholar[2] N. H. Bingman and , J. L. Teugels, Conditions implying domains of attraction, Proceedings of the 7th Conference on Probability Theory, Brasov, 1981, 23–24 Google Scholar[3] N. H. Bingman, , C. M. Goldie and , J. L. Teugels, Regular Variation: Theory and Application, Cambridge Univ. Press, Berkeley, to appear Google Scholar[4] Richard Davis and , Sidney Resnick, Tail estimates motivated by extreme value theory, Ann. Statist., 12 (1984), 1467–1487 86m:62070 0555.62035 CrossrefGoogle Scholar[5] L. De Haan, On regular variation and its application to the weak convergence of sample extremes, Mathematical Centre Tracts, Vol. 32, Mathematisch Centrum, Amsterdam, 1970v+124 pp. (loose errata) 44:3370 0226.60039 Google Scholar[6] E. Haeusler and , J. L. Teugels, On asymptotic normality of Hill's estimator for the exponent of regular variation, Ann. Statist., 13 (1985), 743–756 87h:62067 0606.62019 CrossrefGoogle Scholar[7] Peter Hall, On some simple estimates of an exponent of regular variation, J. Roy. Statist. Soc. Ser. B, 44 (1982), 37–42 83k:62042 0521.62024 Google Scholar[8] W. J. Hall and , J. A. Wellner, Mean residual lifeStatistics and related topics (Ottawa, Ont., 1980), North-Holland, Amsterdam, 1981, 169–184 83k:62136 0481.62078 Google Scholar[9] Bruce M. Hill, A simple general approach to inference about the tail of a distribution, Ann. Statist., 3 (1975), 1163–1174 51:14373 0323.62033 CrossrefGoogle Scholar[10] David M. Mason, Laws of large numbers for sums of extreme values, Ann. Probab., 10 (1982), 754–764 83h:60030 0493.60039 CrossrefGoogle Scholar[11] Richard L. Smith, Estimating tails of probability distributions, Ann. Statist., 15 (1987), 1174–1207 88j:62096 0642.62022 CrossrefGoogle Scholar[12] Jozef L. Teugels, Limit theorems on order statistics, Ann. Probab., 9 (1981), 868–880 83a:62107 0467.62046 CrossrefGoogle Scholar[13] Ishay Weissman, Estimation of parameters and large quantiles based on the k largest observations, J. Amer. Statist. Assoc., 73 (1978), 812–815 80j:62036 0397.62034 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On Estimation of the Scale and Location Parameters of Distribution TailsJournal of Mathematical Sciences, Vol. 262, No. 4 | 24 May 2022 Cross Ref A Discrimination Test for Tails of Weibull-Type DistributionsI. V. RodionovTheory of Probability & Its Applications, Vol. 63, No. 2 | 24 October 2018AbstractPDF (182 KB)Abelian and Tauberian Theorems on the Bias of the Hill EstimatorScandinavian Journal of Statistics, Vol. 29, No. 3 | 1 Sep 2002 Cross Ref Estimating the tail indexAsymptotic Methods in Probability and Statistics | 1 Jan 1998 Cross Ref A Monte Carlo method for estimating the correlation exponentJournal of Statistical Physics, Vol. 78, No. 3-4 | 1 Feb 1995 Cross Ref Extremes in Non-Life InsuranceExtreme Value Theory and Applications | 1 Jan 1994 Cross Ref Weak Convergence of the Hill Estimator ProcessExtreme Value Theory and Applications | 1 Jan 1994 Cross Ref Bayes Quantile Estimation and Threshold Selection for the Generalized Pareto FamilyExtreme Value Theory and Applications | 1 Jan 1994 Cross Ref Asymptotics of T-EstimatorsTheory of Probability & Its Applications, Vol. 37, No. 4 | 17 July 2006AbstractPDF (1051 KB)Limit distributions for compounded sums of extreme order statisticsJournal of Applied Probability, Vol. 29, No. 03 | 14 July 2016 Cross Ref Limit distributions for compounded sums of extreme order statisticsJournal of Applied Probability, Vol. 29, No. 3 | 14 July 2016 Cross Ref Modeling large claims in non-life insuranceInsurance: Mathematics and Economics, Vol. 11, No. 1 | 1 Apr 1992 Cross Ref Rapid variation with remainder and rates of convergenceAdvances in Applied Probability, Vol. 22, No. 04 | 1 July 2016 Cross Ref Rapid variation with remainder and rates of convergenceAdvances in Applied Probability, Vol. 22, No. 4 | 1 July 2016 Cross Ref The empirical distribution function as a tail estimatorStatistica Neerlandica, Vol. 44, No. 2 | 1 Jun 1990 Cross Ref Asymptotic Normality of Hill’s EstimatorExtreme Value Theory | 1 Jan 1989 Cross Ref Volume 31, Issue 3| 1987Theory of Probability & Its Applications375-562 History Submitted:04 February 1986Published online:28 July 2006 InformationCopyright © 1987 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131060Article page range:pp. 463-469ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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