  Based on the methods provided in Caeiro and Gomes (2002) and Fraga Alves
(2001), a new class of location invariant Hill-type estimators is derived in
this paper. Its asymptotic distributional representation and asymptotic
normality are presented, and the optimal choice of sample fraction by Mean
Squared Error is also discussed for some special cases. Finally comparison
studies are provided for some familiar models by Monte Carlo simulations.
