Robust tests for Pareto density estimation

Abstract

A common practice to determine the extension and heaviness of heavy tails of income, return and size distributions is the sequential estimation and fitting of one or several models, starting from a group of the largest observations and adding one observation at a time [14]. In the early stages this kind of procedure shows high sensitivity of the shape parameter estimates to single observations, the end of the search being fixed when the shape parameter value estimates reach a plateau. In this paper we propose a stepwise fitting of a heavy-tailed model, the Pareto II distribution [1], previously applied to the size distribution of business firms. The procedure, based on the forward search technique [2], is data-driven since observations to be added at each iteration are determined according to the results of the estimation carried out at the preceding step and not, as in sequential fitting, according to their rank. © Springer-Verlag Berlin Heidelberg 2011.