Zhaozhi Fan
Estimation Problems for Distributions with Heavy Tails
Preprint series: Mathematica Gottingensis

MSC:

60E07 Infinitely divisible distributions; stable distributions

62F12 Asymptotic properties of estimators

Abstract: This dissertation presents new estimation methods for the tail index
of heavy-tailed distributions. Estimators with U-statistics structure have been
developed. Another estimator is constructed by using resampling techniques.
A large deviation principle and the asymptotic normality of the estimators are proved.
Simulation studies show that the convergence rates of the new estimators are
better than those of the so far existing ones.

Keywords: Parameter estimation, Heavy-tailed distributions, Stable distributions, Large deviation principle, U-statistics, Resampling method