Empirical Spectral Analysis of Gaussian Homogeneous Random Fields

Estimates of the spectral densities of Gaussian homogeneous random fields specified on two-dimensional and $p$-dimensional integer-valued lattices are investigated. The parameters are found for the weighting functions of the spectral density estimates so as to minimize the mean-square error of estimation (or its upper bound) under given a priori assumptions regarding the degree of smoothness of the estimated spectral density.