Asymptotic Normality of Hill Estimator for Truncated Data

Arijit Chakrabarty (Indian Statistical Institute)


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.

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Pages: 2039-2058

Publication Date: October 31, 2011

DOI: 10.1214/EJP.v16-935


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