  In extreme value theory, there are two fundamental approaches, both widely
used: the block maxima (BM) method and the peaks-over-threshold (POT) method.
Whereas much theoretical research has gone into the POT method, the BM method
has not been studied thoroughly. The present paper aims at providing conditions
under which the BM method can be justified. We also provide a theoretical
comparative study of the methods, which is in general consistent with the vast
literature on comparing the methods all based on simulated data and fully
parametric models. The results indicate that the BM method is a rather
efficient method under usual practical conditions. In this paper, we restrict
attention to the i.i.d. case and focus on the probability weighted moment (PWM)
estimators of Hosking, Wallis and Wood [Technometrics (1985) 27 251-261].
