Electronic Journal of Probability

Asymptotic Normality of Hill Estimator for Truncated Data

Arijit Chakrabarty

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Abstract

The problem of estimating the tail index from truncated data is addressed in [2]. 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 [11]. Motivated by this, we show the same in the truncated case for that class.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 74, 2039-2058.

Dates
Accepted: 31 October 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820243

Digital Object Identifier
doi:10.1214/EJP.v16-935

Mathematical Reviews number (MathSciNet)
MR2851055

Zentralblatt MATH identifier
06049130

Subjects
Primary: 62G32: Statistics of extreme values; tail inference

Keywords
heavy tails truncation second order regular variation Hill estimator asymptotic normality

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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