An L2 -test for comparing spatial spectral densities

We consider Z1 and Z2 second-order stationary spatial processes. Our goal is to test whether the dependence structure is the same for both processes, that is, H0:f1=f2, where each fl denotes the spectral density of each observed process, for l=1,2. We study the asymptotic distribution for a Cramer-von-Mises type test statistic, under H0 and under local alternatives. A simulation study showing the performance of the test is also provided.