Testing the covariance function of stationary Gaussian random fields

In many problems, a specific function like h(⋅)h(⋅) is considered as the covariance function. Based on the asymptotic distribution of the periodogram and Euler characteristic, three methods are introduced to test the equality of the covariance function with h(⋅)h(⋅). Our analyses prove the accuracy of the power and scaling laws for the covariance function of metal surfaces.