can be improved by borrowing strength across nearby locations. While methods for univariate extreme data are well developed, modeling spatially-referenced extreme data is an active area of research. Max-stable processes \[@dehaan-2006a\] are the natural infinite-dimensional generalization of the univariate generalized extreme value (GEV) distribution. Just as the only limiting distribution of the scaled maximum of independent univariate random variables is the GEV, the scaled maximum of independent copies of any stochastic process can only converge to a max-stable process. Max-stable process models for spatial data may be constructed using the spectral representation of @dehaan-1984a. Max-stable processes built from this representation were first used for spatial analysis by @smith-1990a. Since then, a handful of subsequent spatial max-stable process models have been proposed, notably that of @schlather-2002a and @kabluchko-2009a, who proposed a more general construction that includes several other known models as special cases. Applications of spatial max-stable processes include @coles-1993a, @buishand-2008a, and @blanchet-2011.

Because closed-form expressions for the likelihoods associated with spatial max-stable processes are not available, parameter estimation and inference is problematic. Taking advantage of the availability of bivariate densities, @padoan-2010a suggest maximum pairwise likelihood estimation and asymptotic inference based on a sandwich matrix (composed of expected derivatives of the 