Dr. Emanuele Taufer (University of Trento and UCSB)

Title: Semi-parametric estimation of the tail index of a distribution

Abstract: The concept of regularly varying function is an essential analytical tool for analyzing data in economics and finance, since a remarkable number of regularities, or “laws”, are considered to follow an approximate power law, at least in the upper tail, in these fields. Available estimators of the tail index of a distribution are usually based on extreme order statistics which are often too few to provide exhaustive information on the problem. In the talk, a different approach, based on a regression-type estimator, which utilizes all sample data will be considered. The method discussed exploits the fact that, under some conditions, the behavior of the distribution function near infinity is reflected in the behavior of the characteristic function near the origin. The approach is semi-parametric as only an assumption about the tail of the distribution is used. Theoretical properties of the estimator, including its bias, variance and asymptotic distribution are derived as well as rules for its practical application. 

This is a joint work with Mofei Jia (University of Trento)