Several new tail index estimators
Abstract
In the paper we propose some new class of functions which is used to construct tail index estimators. Functions from this new class is non-monotone in general, but presents a product of two monotone functions: the power function and the logarithmic function, which plays essential role in the classical Hill estimator. Introduced new estimators have better asymptotic performance comparing with the Hill estimator and other popular estimators over all range of the parameters present in the second order regular variation condition. Asymptotic normality of the introduced estimators is proved, and comparison (using asymptotic mean square error) with other estimators of the tail index is provided. Some preliminary simulation results are presented.
Cite
@article{arxiv.1501.00811,
title = {Several new tail index estimators},
author = {Vygantas Paulauskas and Marijus Vaičiulis},
journal= {arXiv preprint arXiv:1501.00811},
year = {2015}
}
Comments
submitted for publication