Electronic Journal of Probability

Asymptotic Normality of Hill Estimator for Truncated Data

Arijit Chakrabarty

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

heavy tails truncation second order regular variation Hill estimator asymptotic normality

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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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