Regression estimator for the tail index

Abstract: Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was aimed by recent works with different methods, for example by using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically consistent, but for tail index $\xi >1$ and smaller sample sizes the estimation fails to approach the theoretical value for realistic sample sizes. In this paper, we introduce a new empirical method, which can estimate high tail index parameters well and might also be useful for relatively small sample sizes.