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

All Block Maxima method for estimating the extreme value index