Resumen de Weiss-Hill estimator

M. Isabel Fraga Alves

• In this paper the asymptotic distributional behaviour is derived for a new estimator for the extreme value index g of a distribution, which is a combination of two estimators proposed by Weiss and Hill (Weiss, 1971, and Hill, 1975). For |g|>1/2, the estimator outperforms the Moment estimator (Dekkers and al.,1989), in the sense that it has a smaller asymptotic variance than the latter; moreover, for g>1/2 (g<0, resp.) the estimator behaves asymptoticaly like the Hill - resp. Weiss - estimator; for |g|<1/2 the estimator does not achieve the same rate of convergence as the Moment estimator. Simulation results concerning the comparison of the mentioned estimators are also presented.