Large deviations of tail estimators based on the Pareto approximation
- 1 September 1987
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 24 (3) , 619-630
- https://doi.org/10.2307/3214094
Abstract
We consider the relative error of a tail functionwhen this is approximated byy–αusing an estimator of Hill's forα.The results combine recent work of Davis and Resnick on tail estimation with Anderson's work on large deviations in extreme-value theory. Treating separately the domains of attraction of Φαand Λ, we obtain general conditions for the relative error to tend to 0 asu→∞,y →∞ simultaneously. The results serve as warning against the automatic extrapolation of estimates based on extreme-value approximations.Keywords
This publication has 14 references indexed in Scilit:
- Estimating Tails of Probability DistributionsThe Annals of Statistics, 1987
- SLOW VARIATION WITH REMAINDER: THEORY AND APPLICATIONSThe Quarterly Journal of Mathematics, 1987
- Large Deviations of ExtremesPublished by Springer Nature ,1984
- Extensions of Regular Variation, I: Uniformity and QuatifiersProceedings of the London Mathematical Society, 1982
- Convergence rates for the ultimate and pentultimate approximations in extreme-value theoryAdvances in Applied Probability, 1982
- Uniform rates of convergence in extreme-value theoryAdvances in Applied Probability, 1982
- A Simple General Approach to Inference About the Tail of a DistributionThe Annals of Statistics, 1975
- Statistical Inference Using Extreme Order StatisticsThe Annals of Statistics, 1975
- On R. Von Mises' Condition for the Domain of Attraction of $exp(-e^{-x})^1$The Annals of Mathematical Statistics, 1972
- The Rate of Growth of Sample MaximaThe Annals of Mathematical Statistics, 1972