Permutation bootstrap and the block maxima method

Aline Mefleh (1, 2) , Romain Biard (1) , Clément Dombry (1) , Zaher Khraibani (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 UL - Université Libanaise, Faculté des Sciences Section (1) Hadath-Beyrouth

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.

Mots clés: block maxima method; extreme value theory; permutation bootstrap; ranks

Domaines: Probabilités [math.PR]

Aline Mefleh, Romain Biard, Clément Dombry, Zaher Khraibani. Permutation bootstrap and the block maxima method. Communications in Statistics - Simulation and Computation, 2021, 50 (1), pp.295-311. ⟨10.1080/03610918.2018.1563146⟩. ⟨hal-01998521⟩