Asymptotic Properties Of Moment-type Estimators Of The Extreme Value Index

This thesis considers the asymptotic properties of extreme value index estimators.In the first part of this paper, based on the asymptotic expansion of M_n^α(α> 0), a moment-type estimator of extreme value index is established, which is:wherewithα> 0 and (-1)^αis meaningful. The asymptotic properties of this kind of moment-type estimator are proved under the second order conditions.In the second part of this paper, a new kind of location invariant momenttypeestimator is proposed,ie.,whereThe asymptotic properties of (?),₃(k₀,k) such as strong and weak consistency, asymptotic normality are considered under some conditions.