Abstract
For iid observations from a common distribution Fwith regularly varying tail , a popular estimator of α is the Hill estimator. Regular variation of the distribution tail is equivalent to weak consistency of the Hill estimator in a manner made precise in Mason (1982) but necessary and sufficient conditions for asymptotic normality of this estimator are still somewhat shrouded in confusion. This is in part due to the different possibilities for a centering in the asymptotic normality statement. We clarify the roles played by smoothness conditions such as Von Mises conditionsfor the asymptotic normality and give a minimal condition under which a non constant centering can be used
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