  The core of the classical block maxima method consists of fitting an extreme
value distribution to a sample of maxima over blocks extracted from an
underlying series. In asymptotic theory, it is usually postulated that the
block maxima are an independent random sample of an extreme value distribution.
In practice however, block sizes are finite, so that the extreme value
postulate will only hold approximately. A more accurate asymptotic framework is
that of a triangular array of block maxima, the block size depending on the
size of the underlying sample in such a way that both the block size and the
number of blocks within that sample tend to infinity. The copula of the vector
of componentwise maxima in a block is assumed to converge to a limit, which,
under mild conditions, is then necessarily an extreme value copula. Under this
setting and for absolutely regular stationary sequences, the empirical copula
of the sample of vectors of block maxima is shown to be a consistent and
asymptotically normal estimator for the limiting extreme value copula.
Moreover, the empirical copula serves as a basis for rank-based, nonparametric
estimation of the Pickands dependence function of the extreme value copula. The
results are illustrated by theoretical examples and a Monte Carlo simulation
study.
