Matsui, Muneya4; Mikosch, Thomas Valentin5; Tafakori, Laleh6
1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Nagoya University3 Shiraz University4 Nagoya University5 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet6 Shiraz University
If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimators of the tail index of a distribution to data which are rounded off one often observes that these estimators oscillate strongly as a function of the number k of order statistics involved.We study this phenomenon in the case of a Pareto distribution. We provide formulas for the expected value and variance of the Hill estimator and give bounds on k when the central limit theorem is still applicable. We illustrate the theory by using simulated and real-life data.