Extreme value theory is an issue extensively applied in many
different fields. One of the central points of this theory is
the estimation of a positive extreme value index. In this paper we
introduce a new family of block type statistics related to this
estimation. A weak consistency of the introduced statistics is
proved. A bivariate central limit theorem for newly introduced
statistics is derived. We provide the new family of semi-parametric
estimators for the positive extreme value index. Asymptotic
normality of the introduced estimators is proved. It is shown that
new estimators have better asymptotic performance comparing with
several block-type estimators over the whole range of parameters
presented in the second order regular variation condition. An
application to the estimation of the positive valued extreme value
index for several real data sets is provided.
