Almost sure convergence of the Hill estimator
- 1 September 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 104 (2) , 371-381
- https://doi.org/10.1017/s0305004100065531
Abstract
In this note we characterize those sequencesknsuch that the Hill estimator of the tail index based on theknupper order statistics of a sample of sizenfrom a Pareto-type distribution is strongly consistent.Keywords
This publication has 14 references indexed in Scilit:
- Estimating Tails of Probability DistributionsThe Annals of Statistics, 1987
- A Law of the Iterated Logarithm for Sums of Extreme Values from a Distribution with a Regularly Varying Upper TailThe Annals of Probability, 1987
- Strong laws for the k-th order statistic when k≦c log2 nProbability Theory and Related Fields, 1986
- A Semigroup Approach to Poisson ApproximationThe Annals of Probability, 1986
- Kernel Estimates of the Tail Index of a DistributionThe Annals of Statistics, 1985
- On Asymptotic Normality of Hill's Estimator for the Exponent of Regular VariationThe Annals of Statistics, 1985
- Extreme Values in Insurance MathematicsPublished by Springer Nature ,1984
- The law of the iterated logarithm for normalized empirical distribution functionProbability Theory and Related Fields, 1977
- A Simple General Approach to Inference About the Tail of a DistributionThe Annals of Statistics, 1975
- A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of ObservationsThe Annals of Mathematical Statistics, 1952