On the Estimation of the Extreme-Value Index and Large Quantile Estimation
Open Access
- 1 December 1989
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 17 (4) , 1795-1832
- https://doi.org/10.1214/aos/1176347396
Abstract
This paper consists of two parts. An easy proof is given for the weak consistency of Pickands' estimate for the main parameter of an extreme-value distribution. Moreover, further natural conditions are given for strong consistency and for asymptotic normality of the estimate. Next a large quantile of a distribution is estimated by a combination of extreme or intermediate order statistics. This leads to an asymptotic confidence interval.Keywords
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