Two Classes Of Semi-paranmetrie Estimators And A Location Invariant Estimator Of The Heavy-tailed Index

There have been many studies show that, in fact, Heavy-tailed models are quite useful in the most diversified areas of application, like insurance, telecommunication networks, biostatistics. finance and computer science, among others. Therefore, we must do further research for heavy tail distribution. make more robust. more effective estimators for the heavy tail index.In this paper, the Extreme value theory and the Regular variable variable theory, which respectively are the theoretical foundations of the heavy tail index estimating and the properties studying, are introduced systematically. In addition, some common and classic estimation methods for the extreme value index (or the heavy tail index) are also presented. On the basis of previous studies, we also provide the new two classes of semi-parametric estimators and a location invariant estimator. Furthermore, their asymptotic distributional behaviors are derived. We also do simulation for the new two classes of estimators, and compare them respectively with the estimator Γn,k1/α((g,α) and the Hill estimator. The results found that, under certain conditions, the two classes of the new estimators has certain advantages, closer to the real value.