Asymptotic normality of Hill Estimator for truncated data

Details Asymptotic normality of Hill Estimator for truncated data Asymptotic normality of Hill Estimator for truncated data

2010-09-22

arxiv.org/abs/1009.4286v1

Mathematics

Statistics Theory

Scientific paper

The problem of estimating the tail index from truncated data is addressed in Chakrabarty and Samorodnitsky (2009). 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, it is well known that asymptotic normality of the Hill estimator follows from the assumption of second order regular variation of the underlying distribution. Motivated by this, we show the same in the truncated case in light of the second order regular variation.

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