On Location Invariant Hill-type Estimators For Heavy Tailed Distribution

It has been proved that the data of finance, insurance, hydrology, environmental, soci-ology and so on are not normal distributions. They often show the characteristics of peak and thick tail. How to depict the tail features, that is how to estimate the tail index of heavy-tailed distribution, becomes the focus of academic concern.In the paper, firstly, we detailed the theoretical basis of heavy-tailed distributionsâ†'the extreme value theory and some classic estimators for heavy tailed index. On the foundation of Mn(α)(k0, k), a new Hill-type estimator is studied, which is location invariant. Its asymptotic distributional behavior is derived under the regular variable conditions and its asymptotic distributional representation is presented.Beside this we also discuss the selection of the parameter k0considering the Mean Squared Error.At last comparison studies are provided for some familiar models by Monte Carlo simulations and γn(1)(k0, k, α) is better than γn(h)(k0, k) under the special condition.