Abstract: We analyze the behavior of the Hill statistic applied to data coming from a truncated power law, assuming that the truncating threshold goes to infinity along with the sample size. It turns out that if the growth rate of the threshold is sufficiently slow, then a priori choosing a 'k' so that the Hill statistic is consistent is a problem. To overcome this, we suggest a sample based (and hence random) choice of 'k'. In this talk, we shall show that this choice of 'k' leads to a consistent estimator of the inverse of the tail exponent, and also show that under some further assumptions, the Hill statistic is asymptotically normal.

This is a joint work with Gennady Samorodnitsky.