ASYMPTOTIC PROPERTIES OF GENERALIZED DPR STATISTIC

作者：Vaiciulis Marijus^*

来源：Lithuanian Mathematical Journal, 2012, 52(1): 95-110.

• asymptotic normality
• DPR estimator
• Hill estimator
• Pickands estimator
• mean-squared error
• tail index

We investigate asymptotic properties of the so-called generalized Davydov, Paulauskas, and Rackauskas statistic that was introduced in [V. Paulauskas and M. Vaiciulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36-50,2011]. We obtain an asymptotics of the bias of this statistic and show that this statistic is asymptotically normal. As an application, we provide a new class of semiparametric heavy-tailed estimators and compare these estimators with other estimators, including the popular Hill and Pickands estimators.

• 出版日期2012-1