Permutation bootstrap and the block maxima method

We present a permutation bootstrap method for reducing the variance of estimation in the so-called block maxima (BM) method in extreme value theory. In the case of independent and identically distributed observations, it is sensible to use the permutation bootstrap to reduce the variance of the parameter and quantile estimators. The method is analyzed and we propose an implementation of the permutation bootstrap based on a particular sampling from the data based on the BM-ranks whose distribution is derived and easy to simulate. The performance of the method is discussed in a numerical study on simulated and then real data.