Asymptotic Normality of Hill Estimator for Truncated Data

Arijit Chakrabarty
2011 Electronic Journal of Probability  
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, it is well known that asymptotic normality of the Hill estimator follows from the
more » ... 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. 1991 Mathematics Subject Classification. 62G32.
doi:10.1214/ejp.v16-935 fatcat:q3w7ejvnmzcotapbqs2vplzxi4