  The block maxima (BM) approach in extreme value analysis fits a sample of
block maxima to the Generalized Extreme Value (GEV) distribution. We consider
all potential blocks from a sample, which leads to the All Block Maxima (ABM)
estimator. Different from existing estimators based on the BM approach, the ABM
estimator is permutation invariant. We show the asymptotic behavior of the ABM
estimator, which has the lowest asymptotic variance among all estimators using
the BM approach. Simulation studies justify our asymptotic theories. A key step
in establishing the asymptotic theory for the ABM estimator is to obtain
asymptotic expansions for the tail empirical process based on higher order
statistics with weights.
