A class of unbiased location invariant Hill-type estimators for heavy   tailed distributions
  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. 
Jiaona Li, Zuoxiang Peng, Saralees Nadarajah