Abelian and Tauberian Theorems on the Bias of the Hill Estimator

Segers, Johan
(2002) Scandinavian Journal of Statistics : theory and applications — Vol. 29, n° 3, p. 461-483 (2002)

Files

AbelianandTauberianTheoremsonthebiasofthehillestimator.pdf
  • Restricted Access
  • Adobe PDF
  • 214.41 KB
Request a copy

Details

Authors
Abstract
The bias of Hill's estimator for the positive extreme value index of a distribution is investigated in relation to 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 generalized 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 certain rates. A comparison with second-order conditions encountered in the literature is made.

Citations

  • APA
  • Chicago
  • FWB

Segers, J. (2002). Abelian and Tauberian Theorems on the Bias of the Hill Estimator. Scandinavian Journal of Statistics : theory and applications, 29(3), 461-483. https://doi.org/10.1111/1467-9469.00301 (Original work published 2002)