  Likelihood inference for max-stable random fields is in general impossible
because their finite-dimen\-sional probability density functions are unknown or
cannot be computed efficiently. The weighted composite likelihood approach that
utilizes lower dimensional marginal likelihoods (typically pairs or triples of
sites that are not too distant) is rather favored. In this paper, we consider
the family of spatial max-stable Brown-Resnick random fields associated with
isotropic fractional Brownian fields. We assume that the sites are given by
only one realization of a homogeneous Poisson point process restricted to
$\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these
sites. As the intensity increases, we study the asymptotic properties of the
composite likelihood estimators of the scale and Hurst parameters of the
fractional Brownian fields using different weighting strategies: we exclude
either pairs that are not edges of the Delaunay triangulation or triples that
are not vertices of triangles.
