Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 74, 2039-2058.
Asymptotic Normality of Hill Estimator for Truncated Data
The problem of estimating the tail index from truncated data is addressed in . In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untruncated situation, asymptotic normality of the Hill estimator is well known for distributions whose tail belongs to the Hall class, see . Motivated by this, we show the same in the truncated case for that class.
Electron. J. Probab., Volume 16 (2011), paper no. 74, 2039-2058.
Accepted: 31 October 2011
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G32: Statistics of extreme values; tail inference
This work is licensed under aCreative Commons Attribution 3.0 License.
Chakrabarty, Arijit. Asymptotic Normality of Hill Estimator for Truncated Data. Electron. J. Probab. 16 (2011), paper no. 74, 2039--2058. doi:10.1214/EJP.v16-935. https://projecteuclid.org/euclid.ejp/1464820243