Asymptotic Properties Of The Tail Index Estimator And The Second Order Parameter

In the first part of this paper,a new kind of location invariant moment-type tail index estimator is proposed,which is where for j=1,2 andThe asymptotic properties such as strong and weak consistency,asymptotic normality were considered under some conditions.The asymptotic distributional represention and Edgeworth expansions of the distribution of this new class Moment type tail index estimator were also derived under the second regular variation conditions.Comparison studies with some well-known index estimators was provided by Monte Carlo simulation.In the second part of this paper,based on the second regular varying condition and a statistic related to the second parameter,we established a class of semi-parametric estimator of the second order parameter,which isρThe Consistency and asymptotic normality of the second order parameter estimator, respectively,are proved under the second order condition and the third order condition.Simulation studies was also provided.